If an 8 might attacks my 9 might holding, can he then instantly bellows breathe and kill my unit?

It depends on when he plays it.

• During the Showdown, before combat damage: Yes. Bellows Breath deals 1 damage (2 with Repeat), and that damage stays marked through combat (damage only clears at Combat Cleanup/end of turn). Combat then adds the attacker's 8 Might → 9 damage on your 9-Might unit = lethal, it's killed.

• After combat resolves: No. Combat Cleanup heals all units in play first (Rule 461.1.a.1), wiping the 8 damage before anyone can play a new spell. A fresh 1 damage on a 9-Might unit is nowhere near lethal.

Bellows Breath is an [Action] that can be played in showdowns, so the pre-damage window is real — but "instantly" after the hit won't work, because the heal beats him to it.