What is the True Vault Hunter Mode?
The main difference that you will notice is the inclusion of Tiny Tina into Athena's narration of the story. The enemies will of course be scaled up based on the area that you are playing in (scaled to your level in UVHM) and some will have shields or armour now. The loot will be of higher quality but RNG is RNG, i have found the easiest way to get a legendary you want is just by farming the sentinel or Iwajira for a slightly higher chance of a legendary that you don't want, then hitting the grinder. on the quest side of things the jumps in levels between the quest are a fair bit steeper than in BL2 and you will need to do side quests or farming bosses instead of simply relying on quests alone to level up. When it says level up higher, it means you will level up faster than in the first play through as you can level up past the recommended level (if you enjoy killing enemies for a measly 1xp. That is about it for TVHM.