This is earned by defeating 100 agents in Survivors mode, whether it is in Team Match or Death Match, and can be done in either Ranked or Player matches. An agent is any other human character, like Chris or Ada; it is not required to kill just the Agent character for this achievement. Kills are cumulative over all your games.
Kills are earned by defeating another agent as an agent, or defeating an agent as an enemy character (zombie, J'avo, etc.). At the end of each match, the game will display how many kills you've earned alongside you deaths.
You can track your total kills under Records. There is an entry for agents defeated in the section for Survivors.
The mode itself can be frustrating, as it is easy to get downed pretty quickly. If going for this legitimately, play a character with a strong weapon like Agent, and try to pick up the Grenade Launchers, Rocket Launchers or Elephant Killers that will spawn around the map. Try to hang back from the action and let others whittle their health down so you can swoop in and finish them off.
This can be boosted in a 1v1 player match. Set the number of players to 2, make one slot private, and invite a friend. Meet up in a designated spot and take turns killing each other. Most rounds should last less than 30 seconds this way, so it wouldn't take too long to get the amount of kills you need.