Borderlands – Which is better: side quests after killing the warrior or Playthrough 2

His crit spots are his Heart, his mouth and his...ribs? on his sides.

Here he his with a hole in his heart, taking some crit damage:

I tried to get a good pic of his ribs/side weak spot but they didn't come out clearly.

All crit spots save for the mouth are covered by hard, destructible rock; they're pretty noticable and just scream "weak point". Keep shooting them and they'll break, showing liquid lava underneath. All of his crit points are lava. His mouth isn't armored, but it's much harder to hit as it's always moving and nor always in an easy to shoot spot. I think, but I'm not sure, that his mouth takes more damage from shots than his heart. A good sniper can get a few good hits in there, but otherwise I wouldn't recommend it.

Note that the armor covering his heart and arm weakpoints regenerates every time he goes in the lava, which he does after taking so much damage. After you break the armor over his heart he'll go back under the level soon, so be quick. If you're precise and break just one chunk of armor and keep hitting the weak spot you'll have more time to deal critical damage than if you break all the armor around his heart, so be precise if at all possible.

Not some weapons like rocket launchers and other splash-damage weapons won't crit. Try a sniper rifle to confirm that you're getting crits. If your weapon isn't capable of getting critical hits, I recommend switching to one which can. Warrior takes significantly reduced damage anywhere but his crit spots, and even direct hits on his weak spots with non-crit damage won't hurt him much.

In general, your build in early game does not matter much. Just make sure you phaselock those mutants as often as you can. If you are still uncomfortable with your build, try shifting into Harmony to heal better.

As for money, no, you can't store it in the bank, but just stop caring! Every time you die, you lose 7% of your current money—the less you have, the less you should be afraid of dying. I've never had problems with money—even if you miss that rare gun in the shop, it is not like you won't find a better one soon.

There even is a reason and a way to keep you money low voluntarily: Slot machines. There's a low but reasonable chance to win Eridium there, and as cost of playing rises with the level of main quest, there's zero point in saving for later—money inflates, Eridium doesn't! My personal way of playing is to burn all my money in slots after each trip to battlefield. Longest forays usually net me mostly two to three "rounds"—that is, gambling sessions that end in full inventory (of course, buy inventory upgrades first).

Gamble!

• No money - no fear of death!
• Accidental good gun!
• Average of 0.1916 bars of Eridium per pull!
• Eventual "Jackpot!" badass challenge!

The only thing you need a lot of money for is "For the Hoard!" achievement - and accumulating 3,000,000 is fairly easy even at the end of Normal, and trivial at the end of TVHM.