So, I recently beat the game's normal mode for the first time.
Jack was an absolute pushover, to the point where I'm pretty sure I did something wrong and/or brilliant.
I dropped my nuke-turret next to him the moment the fight started, and drilled a round into his noggin and a couple more into his chest and then the cutscene triggered.

The Warrior pretty much threw me into the lava right away and I couldn't get out in time, though. Which ended up being okay because I found a couple of outcroppings of cover could hide behind and just put bullets into him to my heart's content until his health finally dropped down to zero.

Underwhelming final boss fights! Go!
I'm having more trouble in Liar's Berg during playthrough 2.