The first encounter you can have with a Butcher is in the Ghost Town area of the Jungle. This achievement can be completed by damaging the Butcher with any weapon type, as long as the final blow comes from an axe.
For example, if you're playing a character like Logan or Purna who does better with long range attacks, you can shoot a Butcher from a distance until its health is low, than get in close with an axe (or throw it) to get the last bit of damage.
More Butcher locations, from the Dead Island wiki:
"Jungle:
- Russian's Bunker.
- Outside Overpass Camp where a massive crash can be found.
- Can be found sometimes at one of the abandoned Jungle Shacks.
- Smugglers' Den (Where the vehicle and caravan crashed at).
- One can be found at the top of the Jungle Muggers cave mountain camp.
Laboratory:
- Many can be found in different areas of the Laboratory.
- Ope's Cave.
- Three can be found in Tomb of Natives in the Definitive edition of the game."
Butchers also spawn in some waves of the Arena.