For this achievement you need 1000 monster kills. While there are some places to farm this (there is a spot you'll come across in the Ice Cave where you are forced into a fight that generally has 6+ enemies, you can walk off and on this square to keep fighting) you'll likely get this without trying assuming you aren't attempting a speed run.
Even if you speed run the main game and just do the bonus dungeons after, you should still get it. If not, that spot in the Ice Cave I mentioned further up works well.