With a cap on bonus actions, the bosses can’t destroy your entire team in one turn. You’re going to get some chances at using your own abilities. So here are some that might be useful:
Flash Bomb - build up some stun on those bosses so you can do some big damage.
Haste - more speed = more often you can get a hit in.
No Guard - want to do massive damage? Use flash bomb, build up some stun, then use no guard and get some massive hits in. You would have died anyway when the boss gets a turn, so no guard wouldn’t hurt.
Void spells - nullify some boss damage.
Volatile - use a monster like puffoxin, so when you die the boss takes big damage.
Plague - slow the boss down.
Weakness - okay, this is not an ability. But make a team of enemies that are strong against that boss.
Guardian - tanks can take a lot of hits. Let them take all the bonus actions.
Timestrike - major damage after the enemy uses a high TU attack.
Stun Skin - stun and kill off bonus actions when your monster dies.
Heavy Hitters - again, not an ability, but if you’re facing one boss, then put monsters that do major damage to one enemy as opposed to enemies that do moderate damage to the whole field.
Last Stand - useful if you get a chance. Good when paired with a stunner if you can pull it off. Use flash bomb on the second to last monster, then go crazy with last stand. You’ll get quite a few hits in.
And by the way, you’ll also need high level monsters. If you find you absolutely can’t win, try leveling your monsters some more. Maybe the quest is meant for a stronger team than you currently have.