You can only get this by playing New Game+ (unlocked by beating regular New Game).
There are required Minibosses to fight in Floors 2, 4, and 6. (The room is directly in the middle of your map, and shows an eyeball for the symbol.)
For Floor 2, there's one worm/centipede like thing that spawns and is pretty easy to beat. On Floor 4, a second centipede will spawn after hurting the first one a little bit and will have some different attacks from the Floor 2 Miniboss and the one you're already currently fighting, but again, is still pretty easy. The Floor 6 Minibosses spawn at the same time as each other (and again, are centipedes lol), and are quite a bit tougher than the ones on Floor 2 and 4, but are easily thwarted with some dodging and the fact that you should have some good upgrades by that point.
To defeat these Minibosses, all you have to do is destroy each part of its body (not including the head) while watching out for the projectiles it shoots at you, and it'll eventually blow up. They don't have much health at all and die fairly quickly, even on Floor 6. I personally got the achievement on Floor 4 during my first New Game+ run, right after beating the third centipede thing, so Idk how random the Miniboss spawns are, but the achievement shouldn't be much of a problem at all.