Thanks to Minioger for the confirmation on this one - so kudos to him!
To confirm - this achievement requires you to level up one of the waves from the game to Level 99.
To do this, you need to firstly finish the 50 original waves. Once the achievement pops for this and you finish Wave 50, you can re-enter any wave you want and play it again.
This achievement requires you to play, and beat, a single wave 99 times.
This is more a grind than anything. Choose the first wave and simply replay it - should take you between 35 and 50 seconds each time.
Rinse and repeat 99 times. The game, thankfully, keeps track of the number of replays.