You need to have 150k Beast Handler XP at once, not a total amount collected. So wait a moment before unlocking those 5th tier upgrades. XP is distributed evenly on all your monkeys at screen at the end of each round, so the more beast handlers you have, the more XP they gain. From my expierience 1-2 standard hard games with only beast handlers (and a village/alchemist) should be enough to earn this achievement.