As the achievement describes, you just have to kill 2000 Purifiers throughout your playthroughs. Now I do not know if this achievement stacks through playing multiple characters, but you can do a new game plus if you've beaten the game and this still counts towards the achievement.
Now this achievement is easy and simple enough, but fairly time consuming. Even after two whole playthroughs in the game I found myself at about 1700 Purifier kills.
The best way I found to farm these kills is to set your game on the easiest difficulty and just keep doing challenge number 9, where you are factioned with the Brotherhood and helping Quicksilver seek revenge after being locked up in the cell. This challenge gives you lots of Purifier kills, and even a Prime Enforcer kill to work towards the Reinforced achievement.
Hope this helps!
EDIT: This achievement actually doesn't stack between different characters, but does between multiple playthroughs of the same character.