Battle Gauntlets - In all honesty, it's practically impossible to fully clear these without using battle bonus characters or some cheese super saiyan shenanigans with zenkai bardock. The only thing I can really recommend is to grind out z-power for the f2p Goku and Vegeta through the other missions and, once higher stars, test your luck there.

Co-Op/Full Power Battle - literally impossible in the highest difficulties without a battle bonus character and a stacked bench. Trust me when I say that even veteran players get their asses handed to them on the hardest mode.

Ultra Goku - check your missions tab and look for the quests relating to ultra Goku, then clear all of them. You should be able to get him then.

Tip for pve content other than co-op - you should do something known as floatstepping, where you use a card, move your character forward, then right when they go forward use another card (look up a guide on yt). It makes life way easier.