If Annihilape ex only has 10HP left, can I use its "Angry Grudge" attack and place all 12 damage counters onto it?
Sure, ka-boom!!! You can put up to 12 damage counters on it even if it doesn't have that much HP remaining. Annihilape ex will do 20x each damage counter that was placed, and at the end of the attack Annihilape ex will be knocked out.
Source: Paldea Evolved FAQ; TPCi Rules Team (2023-06-08)