What you need to know
The Siren doesn't play like other FPS games. The Siren makes full use of Borderlands' elemental effect system and requires a more tactical level of play. Sirens eschew guns that deal the most damage at once for guns that deal elemental effects.
When you start out as a Siren, the benefits aren't obvious. You don't get the elemental guns until you're a decent level (10+). You don't start getting the good elemental guns until a bit later.
You're going to deal less damage per shot compared to other classes. It's really hard to estimate how much damage your elemental effects deal too; don't focus on the numbers, focus on the chaos you wreak. You're going to kill a lot of people, even if it's not in one shot. And in Coop play you're especially valuable; your elemental effects will distract or weaken enemies for your group to finish off easily.
Also, I hope you enjoy the sound of people burning; you're going to hear a lot of it. It's the sound of progress, my friend.
Elements
You need to know elements. Read this, the whole thing. You need to eat, breath and excrete elemental effects.
Your 30% elemental effect chance means any elemental gun with a good rate of fire is a weapon of death in your hands, even if the same gun is near useless for other classes. Experienced players will know this and often offer up elemental guns to Sirens playing Coop. Lots of people don't like/don't understand/can't use elemental guns, so you can get first dibs. This means you won't get first dibs on the high damage, non-elemental guns...but you'll quickly find as a Siren, you don't really want those non-elemental guns anyway. I keep exactly zero non-elemental guns on standby.
Also, explosive isn't an element. Not for a Siren anyway; you get no bonus out of explosive guns, give them to someone else and pick up a gun that can melt some faces.
It's possible to play Siren without focusing on elemental damage...but it just doesn't make much sense. The elemental chance percent boost is insane and costs only 5 skill points for +30% chance per shot.
Patience
Good things come to those who wait. Things like the horrible burning demise of your enemies.
Since elemental guns do Damage Over Time you'll be able to leave an enemy for dead once they've taken enough damage and enough elemental effects have stacked on them for them to die without further gunfire. Take this time to reload more often, duck behind cover to recharge shields, or light up the next target.
As you play you'll get a feel for when an enemy is "done for"; this is the point when the passive elemental Damage Over Time is likely to kill the target with no more direct attacks from you. Watch health bars closely and you'll start to get a sense for this. Don't overkill targets; move on to the next enemy. Enemies with DOT effects shoot less anyway (they're panicked) so just leave them to die and start whittling down the next target.
Note that Shock, Fire and Corrosion all have different effect lengths and guns have different damage per second; you'll need to acquire this feel per gun but you'll be amazed how quickly you start to intuit when an enemy will die. The exact times are listed here, knowing the rough length of the stacked effects will help you estimate when you can stop shooting.
Phase Lock
Phaselock has two primary purposes; to disable a dangerous target for a time so you can focus on other enemies, or to disable a target so you can easily kill it.
Note Phase Lock holds the target still, usually with their Critical point exposed and stationary. This is a great opportunity for you or your teammates to pile on the damage.
Depending on skill tree you can turn Phase Lock into an elemental Area of Effect weapon, a tool for healing yourself/teammates or a way to control enemies (or some combination thereof). They all have their uses, generally I'd pick the Phase Lock variant based on the other skills in the related tree rather than picking the tree just for the Phase Lock skills; all of them work well. Experiment and respec to try all three as you gain enough skill points
Guns
Really the Siren can effectively use any kind of gun; the reload speed, magazine size, bullet velocity and damage boost skills help all guns pretty well. From Rocket Launchers to SMGs you'll be able to hit targets more easily and spend less time reloading. You don't have (explicitly) gun specific skills unlike other classes.
Your gun choice is mostly determined by elemental effects; since your +30% elemental effect chance is per bullet, fast guns make the most sense. In the time it takes to hit one target with an epic Rocket Launcher, you could have stacked insane Fire damage with an SMG of comparable stats and left the target for dead.
Note that most non-Siren players don't like/appreciate/use elemental guns. Many will immediately pass over any Maliwan weapon because, at a glance, they do less damage. You know that's not true, but you can use this to your advantage in coop; most players will willingly give first-dibs on elemental weapons to Sirens. Just ask and make sure it's cool with your friends; you get a lot more out of those guns than they can. If you're playing with other Sirens there may still be loot fights of course.
You will seriously need one gun for each elemental type. I actually keep one SMG and one Sniper Rifle for each elemental type, but try to have at least 3 different elements equipped at once and always be ready to switch to the right element for the job. You don't always need a Slag gun, but be sure to have Fire Shock and Corrosive at the ready.
Note however that your fast reload speed, increased magazine size and reduced damage per bullet (because elemental guns do less straight-up damage) means you're going to run out of bullets. A lot. You're going to want to make sure you have at least 3 or 4 different types of guns (even if you don't keep them all equipped).
Personally I keep around a supply of Sniper Rifles and SMGs with Pistols or Assault Rifles as backups. The SMGs and Snipers run out but I'm never completely out of ammo if I keep 3-4 gun types at once.
Summary
- Use Elemental guns. Only. Keep one of each element.
- Prefer Rapid Fire guns, but other types like Snipers are okay.
- Keep backup guns. You'll run out of ammo for your favorite gun.
- Be cold, calculated and clinical. Don't overkill, let your elemental damage finish off targets.
- Don't worry about doing less damage per hit. You'll know you're doing well because enemies die, not because you deal big numbers of damage at once.
- Use Phase Lock. At the least it keeps Badass enemies out of the fight for a few seconds, at best it's an invaluable tide turning weapon.
- Don't be afraid to play support; Sirens have skills that can be great offensive and defensive support to a whole coop team
The intent of Terramorphous is to be a raid boss, something you bring 4 players along to fight at once. It's possible to beat him with a coordinated team, good equipment, proper skills and tactics (or a reasonable combination of the above), but there's a super cheap slightly helpful way to beat him even solo, too.
The Cheap Way
With The Bee shield and the Conference Call shotgun, Terra is trivial. The Bee adds 40k-50k extra damage per bullet, meaning any good shotgun can do over 500k damage to Terra in one shot. The Conference Call shotgun is optional, but shotguns are best for this method, and the Conference Call is ideal.
The Bee has been significantly nerfed in a recent patch (actually all Amp Shields were) so the amp damage no longer applies to each bullet from multiple bullet weapons (shotguns); instead the damage is split across all projectiles. This means shotguns went from insanely broken with The Bee to being only minorly boosted. Instead try a high Rate of Fire weapon that shoots single bullets per shot (or that fires pellets so close all of them will hit).
You can get The Bee from Hunter Hellquist.
Rapid Fire guns like SMGs work very well. If you can boost shield recharge rate at all, do it; you'll want your shield charged as often as possible, the Bee only kicks in at max shield.
Killing Terra is much harder than it used to be with The Bee but it's still a relatively quick way to do it. The more the merrier though; a team is now almost required so see the tips below rather than hoping on soloing him.
Tips for doing it the right way
Like the mission description says, You Will Die. Even if you take the cheap route, this boss can kill you with a flick of his wrist (tentacle).
Be level 50/max level
This should go without saying, but it's vital. Terra will always spawn at level 50-52. You deal decreased damage to targets higher level than you, so even if you have The Bee and amazing weapons, your damage will be drastically reduced if you're level 45 and Terra is level 52. Save this fight for after your second playthrough to save yourself a lot of grief.
Communicate
Everyone should use headsets if possible. You don't have time to type (don't try, you'll get killed and piss everyone off), use headsets or just play in silence. Coordination is key for doing things live reviving allies
Respec your skills
Lots of skills are useless in this fight. Kill skills aren't great (but you will have tentacles to kill), anything that requires multiple kills isn't great. Elemental damage isn't helpful. Abilities that benefit your team over yourself are often helpful, like the ability that turns Phaselock into an instant revive. Note that no part of Terra can be phaselocked, so keep Phaselock for Revives. Use Decepti0n to trick Terra while reviving allies.
Hug the wall
There's a cliff face on one side of the arena; all players should gun this wall unless running from an attack or grabbing ammo/health (tentacles drop a lot). Spread out a bit so he can't kill you all at the same time. Standing high on the outcropping near the wall will avoid Terra's direct attacks. There's also a little niche where one player can hide from some tentacle attacks. If you don't hug the cliff, Terra's knockback can often knock you off the edge of the arena for an instant kill.
Manage your respawning
Like Crawmerax before him, Terra has a slow elevator leading up to him. After being used it takes a minute or two (seriously, not "a few seconds" or "a little bit") to shoot all the way up. If two players die, make sure you both get on the elevator at once or one of you will be waiting a long time to get back in.
Get back in the fight as soon as possible though, as soon as no single player is alive (or in Fight For Your Life) in Terra's arena, his health resets to max. Be quick but be reasonable; if another player is about to die, wait a couple seconds for them to spawn and use the elevator together. Buy ammo if absolutely necessary, but remember his tentacles drop lots of ammo anyway.
Elements
Terramorphous is occasionally elementally charged and will resist the element he shows up as; I've seen him as Shock and Fire, not Corrosive yet but I'm not sure. It's best to not bother with elemental guns, he doesn't appear to take Damage Over Time damage and doesn't seem especially weak to anything. Sirens should spec away from elemental damage.
Terramorphous can occasionally be slagged but he usually resists it. When he's slagged it lasts for about one second instead of 8, so don't bother unless your best gun is already slag.
Guns
Obviously use your best guns. Don't use elemental guns hoping they'll do DOT, but he does seem to take elemental damage normally. There's no particularly fancy strategy here, put a lot of very big bullets into him. Bring different kinds of guns or you'll run out of ammo. Bring at least one long range gun for the tentacles.
Being a Thresher Terra moves a lot and has many relatively small crit spots, so sniping can be trickier, but due to his bulk his crit spots aren't too small.
Wound tentacles, don't kill them unless you need to
The tentacles he spawns can be annoying, but they're great for Second Winds. Generally it's best to just wound them or ignore them, depending on type, and use them for a Second Wind if someone is knocked out. Hurting tentacles hurts Terra, too, but unless you're sniping you're likely to miss the tentacle a lot more than Terra itself.
Note tentacles drop lots of health and ammo though, so kill some just to keep everyone full of ammo.
Loot
Terra drops a lot of whites and greens, a few blues, a couple purples and always drops one orange class mod (it's not as good as you might hope), and apparently has a chance to drop other orange weapons.
Unlike Warrior, Terra drops all his loot in a tight circle around where he dies. There's pretty much zero chance his loot will fall off the map or be stuck in his body, making the looting much less frustrating than Warrior or BNK3R. You can also see all of the items at once, so there's less risk of ninja-looting ("oranges? There's no orange guns over here....")
Comparison to Crawmerax
I'd say Terra is easier than Crawmerax, even ignoring The Bee trick, and certainly less frustrating to fight. His tentacles will rarely kill you unless you fail to evade, as opposed to Craw Maggots which would zip in, kill you, and flee out of range. Getting second winds is easier, and you don't have to worry as much about elemental matches with the minions. The lack of specific weakpoints you have to kill, one by one means it's much easier to hurt Terra; just shoot in his general direction. He soaks up a lot more damage, but it's much easier to hit him.
If player respawns are spread out, getting back into the fight isn't quite as long or annoying as the infamous Crawmerax elevator. And he doesn't drop 50 %$^&ing equalizers every time he does. Generally he's still extremely hard like Crawmerax, but not frustrating. The only annoying "Crawmerax" thing Terra retains is the instant-kill attacks and knocking players off the map (instant kill without a chance to revive!).
Best Answer
Deathtrap is a situation based skill to use. And while the situation comes up quite often in single player, it does not come up that often in co-op play. My overall suggestion is to use Deathtrap less if you find he is in the way that often. You may feel this lessens the effectiveness of your character, but there again so does having 3 other people there to help you out!
I have not seen any Deathtrap skills change his AI pattern to this point yet, but I have not used the heal-shields ability so that may alter it a bit. He will always pick a target (And most often its the most moronic of them all) and then go up and attack it with a melee or ranged attack depending on if the target is land or air based.
That being said there are pretty much two situations that I will release him in (Again, only in co-op I use him All the time when solo due to using the mechromancer's anarchy build).
The overall goal is to use Deathtrap only in situations where you need to control the AI's targeting of yourself and the people you are playing in co-op (or to get rid of an annoying target that is not worth your bullets). Using him in a situation when people are dropping you have to go in with the understanding you are going to be bringing people back up and they are not likely to get second winds.
Hope this helps.