Contrary to the description, you can get this in one stage (if the computer is smart enough). You must get 10 Hyper Modes WITHIN the 10 stages. To activate Hyper Mode, allow 42 blocks to fall onto your side in 2 turns. You'll see the gauge on the left side flash and say, "Perform a successful Beat Drop to activate Hyper Mode." Do this 10 times and the achievement will unlock.
Easy to do on Expert, cuz the cpu will always counter with a Hyper Mode.