I just finished Borderlands 2 on the normal mode and unlocked the true vault hunter mode (TVHM). Do I need to play the game all over again to grind the warrior (final boss) in TVHM or is it possible to try the boss in TVHM without playing entire game again?
Unfortunately, you will have to play through the main storyline again to fight the Warrior in TVHM (and again once you unlock UVHM). You can re-fight the Warrior in NVHM again, of course, but it caps at ~lvl 35 IIRC.
Now that you know the story & such, though, you can choose to ignore more of the side missions, unless they give gear you need/want for your build.
In general, I find that NVHM is generally good for getting the story, without worrying overmuch about your gear. A wide variety of options work well. Then when you replay in TVHM, you may be forced to optimize more with the more buff enemies you encounter (which is good practice if you wish to play UVHM). Plus, you may see things in the story you didn't catch the first time.