The weakest version of the fire based spells is the Fireball, it costs 25 gems and can be bought at the town right after beating the introducion levels (Scuttle Town Main Street) and defeating P.O.O.P T.O.O.Ts. It deals 3 damage, so you need to fire quite a few on the average enemies. Best to replay the Main Street where the enemies barely have any health.
While the achievement doesn't have a precentage, defeating the 10 enemies is cumulative, it only has to happen in the same save file, replays both in normal and hero mode don't reset the counter.
The second version of the fireball (3 in 3 directions at the same time) counts as well but the strongest (flamethrower) is not. If you accidentally bought the strongest version before doing it, you can switch to a weaker version in the item menu.