Credit for this guide goes to the youtuber PowerPyx. Link to their video below the solution.
Whilst this can be done by repeatedly playing any level until you hit the 99 life cap, you can get this quickly on either of the level Bee-Having. On this level, you'll past by beehives that spawn a swarm of bees. Each time you kill these bees before they can leave their hive, you get a free life. From approx. 20 lives, it takes about 10-15 minutes to get the achievement. This can be done at any hive in the level, but the easiest (and the one the video suggests using) is immediately after the first checkpoint.
PowerPyx's video: