While I wanted to complete one of the "Buy the (...) building while having no Upgrades" achievements, I realized that I cannot complete quests that consist of defeating enemies (Hellhounds, Spearmen, Shieldbearers), so I searched through challenges and I found some useful ones for each type of enemy:

Hellhounds: 2-24 (49) ; 2-13 (11)

Spearmen: 3-19 (53) ; 2-22 (26) ; 3-14 (22)

Shieldbearers: 5-7 (30) ; 4-22 (26) ; 3-20 (24)