"If an attacker faints a Pokémon with Aftermath using a contact move, the attacker will lose 1⁄4 of their maximum HP."
I assume you are having trouble against Drifblim. A good way to defeat it is to use a non-contact move. Drifblim is weak to Electric and Ice. A few good Pokemon are:
Pikachu / Raichu. Evolve it at Level 26 when it learns Thunderbolt. You don't even need to evolve it.
Haunter / Gengar. Gengar learns Shadow Ball at Level 33. It outspeed Drifblim and launches a STAB super effective blast of dark energy with a base 130 special attack stat. Boom. Dead Drifblim.
Golem. Rock Blast is learnt at Level 27. Rock is a good type against a flying type.
Any normal type with a special attacking move. All it can do is Minimize and/or gust. A rock move is also good.
But Aftermath isn't a huge problem. Potions can heal you immediately, and it is only for contact move. So yeah, don't stress yourself.