In order to get this achievement, you need to encounter all 27 specimen that can chase you in the game. There are two ways to easily get this.
1. Do an Endless Mode run all the way to room 2500. In between each checkpoint up to this room, you are guaranteed to encounter a new specimen. Specimen 2 (slime dude) is already able to chase you from the beginning, and the Clown can be unlocked in Otto's room by clicking the button near his cage. Here's a vid on how to free the clown:
. If you do this successfully and reach room 2500, you are guaranteed to have gotten the badge before even reaching this point.
2. If you die trying to do number 1, just do endless mode again and keep playing it until you've met every specimen. Remember to free the clown when you get Otto's pizzaria room, as he is one of the specimen that you must encounter for the achievement.