I wouldn't bother with Neem. My approach (if I care enough about the plant to make the effort) is to literally drench every part of the plant with Insecticidal Soap (then rinse it off) - its a contact poison so when the IS touches them, they're dead. Then use a systemic that will kill mealybugs (imidacloprid or dinotefuran). Until the systemic takes affect (that could be a couple weeks), check daily and spray the new mealybugs.
Mealybugs are difficult to eradicate but it is possible with a lot of diligence on your part. I wouldn't have that plant anywhere near my other plants as they do spread by walking across touching leaves and wafting from plant to plant on the breeze you cause when you walk by. Or if you touch the infested plant and then touch another plant or by some go between (your pruners, watering can, ...). Also, the nymphs are so tiny, they can hide in the pores of pots or table tops so future plants in that area could be infested.
Good luck. Your plant has a pretty bad case.