This is by far the most tedious and time-consuming achievement to get, and can take a very long time to get. The best way to get this is Another Face. Simply grab the costume at the start, walk through the checkpoint, then use the costume as soon as its cooldown is done. Walk through the checkpoint (to keep track of how many times you've done it), then reset to the checkpoint. It takes ~10 seconds to have the costume come up, so every 10 seconds or so on the timer represents one use of the costume.
You'll have to quit out of the game after using the costume 100 times and open it back up to actually get the achievement.