Borderlands – Is Pyro Pete part of Hyperion

As you said, these are all the pieces already. If what I'd figure is your question it's easy to answer: "How much damage would I do if I fire for $Length time?"

$Length * $RoF = X rounds
X rounds * $damage = gunDamage
X rounds * $DOT% = avgDotAmount

DoTs are smart in this game, they all have their separate timers and can stack independently from one another. This makes the damage as intuitive as possible:

dotDamage = avgDotAmount * ticks(element)
totalDamage = (gunDamage + dotDamage) * multiplier(element)

As this was far too easy to answer, I can only assume your question would be like
"When can I stop firing, knowing that my DoTs will kill the enemy?" To which the answer would be "Never, unless the target isn't currently affected, then keep firing."

To us human player at least; for all the data is there in the fountain of numbers that spew from the target you are perforating with bullets. Would we be perfect computers, we could see when a new dot starts ticking(it wouldn't have a previous tick before it) and thus know exactly how many ticks are left. Being human, all we can say is "it's on fire" or "it's not on fire." This makes knowing for SURE your target is going to die impossible, the best one could do is make a normal distribution graph(wiki) with the probabilities if your target will die.

If that's really what you'd want, I could run it through some model, but it's still gonna be a pretty useless graph. Input the specific gun and skills you're using, and you could get a graph with probabilities mapped vs dotDamage. Even if you could watch that while shooting things, you can only guess how much health your target has left.

If instead, and my final guess, the question would be "How much do I overkill?" that amounts to the same, as that is also "Amount of dotDamage still to be done."

Various tips:

• Shock does normal damage against flesh/armor, so 1.0x not 0.8x. Shock works just fine against him and makes removing the shield a breeze. Non-elemental works fine against him too I think.
• The Bee really really helps, especially during the start. Aside from the Damage over Time effects, it's extremely easy to dodge Pete's attack if you simply walk backwards and shoot at him.
• Pete can be slagged like a normal enemy for a normal duration. If you have Slag grenades or a skill that slags, use it. Slag guns are far less useful in solo play through.
• His DOT (damage over time) effects never wear off over time, so don't wait for them to go away.
• The water valves open and let you remove the long lasting DOT effects from his novas. walk through the water to remove the DOT effect. The DOT effect is weak but it limits your shield's abilities (read: it removes The Bee's effect)
• Opening the valves spawns a group of Rats or Spiderants. They increase in level by 3 each time they're spawned, ending in 66 I think.
• Consider letting two DOT effects stack before opening the valves. This will limit the leveling up of the mobs from the valves
• Open the south (I think) valve as it has Spiderants. The spiderants are far far easier to deal with than the Rats
• If one spiderant/rat is alive when you turn the valve, no more will spawn. If you can stand leaving a spiderant alive and kite him around like Pete you should be able to water yourself down immediately after each nova no problem.
• There are respawning ammo crates around the arena for a reason. Try and open them every once in a while for health/ammo since he takes a LOT of bullets to kill.
• Some people suggest Fire/Corrosion immunity shields to limit his DOT effect, but later on in the fight he'll be doing both Fire and Corrode DOT every Nova anyway, so unless you've got a fire/corrode immune Bee I wouldn't bother with it trying to immunize yourself.
• Immunity doesn't mean you don't take the DOT damage either, it just significantly reduces it. So you'll still slowly lose health and never have full shields.

In short, use Shock or normal damage, slag him, use the Bee, release Spiderants not rats. Try to always leave a spiderant around to kill for a second wind (and so you can open the valve without washing in more enemies each time). The fight is mostly about managing the non-pete enemies to make sure you can wash off the DOT, can get a second wind but so you don't get swarmed. Pyro Pete isn't actually a big problem except for the loooong fight and the DOT effects, just keep moving and he'll never hit you with anything else. No shields spawn with immunity to both elements (unless there's a unique/legendary I'm unfamiliar with)

He can be soloed, but of course a group really does help. With a group it's much easier to manage the spiderants/rats, he's less focused on one target and it's much easier to open the valves since you can assign one person to always do that.

Here's a video demo of a Siren soloing him: