This achievement is probably easiest with Echidna, but very doable with Human as well.
All hydras on level 1 have 1, 2 or 3 heads. The ones with 1 and 2 heads can be taken out in one hit with the starting weapons that do 1 and 2 damage.
The 3 head hydras can be killed safely with a sabre (which does 3 damage) with any race. The sabre can most of the time be picked up on level 1. Alternatively, the Echidna can use the dagger and machete simultaneously for 3 damage (press 1, 1 and 2 to select both weapons).