Just curious, im sure this is answered somewhere but i havent been able to find it.

How exactly do you do the gauntlet in the arena? ive done the other 3 sections but have yet to ever see anything under the Gauntlet tab.

Likely linked to your Alchemist Rank.

On my first game (not NG+), I had access to it around chapter 8 or 9. It's basically a list of individual challenges for specific characters.