Doing this normally would take a while but thankfully there's a somewhat quicker way to do this with an item called Hunter's Grenade. You will need a couple of other things first.
To begin, you need to unlock the Specialist's Showroom, which is done by giving cells (I'm not sure how many) to The Collector, who can be found in the little hub room you go to in between levels.
Once you've unlocked it at the Collector, the next time you're in the Prisoners' Quarters, you should come across a section of the map with a locked door. The door has a switch on your side (it's not a puzzle to open), and a sign stating you're at the Specialists' Showroom. The Hunter's Grenade should be inside behind one of the gold doors once you purchased it.
When you have the Grenade, continue playing as normal and you'll find that some enemies have a small icon above the heads. Bring them down to 40% health or less and throw the Grenade at them to transform the enemy into its Elite variant. Simply kill it, pick the Grenade up and rinse/repeat until you reach 100.