This achivement is having issues as of august 2023 and appears to have been broken since at least february 2023. A lot of the time pops are not counted.
Normally going into late freeplay (around round 250) with a bloon master alchemist is sufficient. Use ultraboost, jungle drums, and permabrew to speed it up significantly. Double HP moabs also significantly increases the amount of damage done since the insta kill isn't affected.
EDIT: I've done some more testing and it seems like the achievement can't be earned if you quit to menu after building the Bloon Master Alchemist. The achievement should pop upon death after reaching the requisite amount of damage. If you're lucky.