I think it would be cool to have hero related achievements.
BUT
Users would maybe complain that they can't complete every achievement without buying EACH hero.
Each hero could get 2 of them.
Here are some examples:
Gerald: Let Gerald reflect 6 attacks in a row (mirror shield)
King Denas: Complete a level with 3.000 gold left (pay your taxes)
Ingvar: Let Ingvar kill 10 Werewolves in bear form (i am the wild one)
Karkinos: Kill 10 Crabs with Karkinos (crab suzette)
Faustus: Let Faustus, Ashbite and Beresad kill 150 enemies at the Arcane Quarters in a single run (True dragon rage)