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.