I found the Kinect imprecise for this mini-game (although it's superior for the action sequences) so I used a controller with the speed set to "high."
To get the achievement, you have to speak to the tall doctor, Roland Walken, who first appears on the plane. When you speak to him there will be a blue dialogue box you can click which will begin the Clover Attack minigame. there are four types of objects to grab:
1. Green clovers are worth one or two points depending on size
2. Rainbow clovers are worth three points
3. Snowflakes briefly freeze everything on screen and double their point value
4. Pink petals gather all clovers on screen together in a whirlwind in the middle
My strategy is to hover on the top of the screen, sweeping left to right as I dodge the lightning bolts. I prioritize fast-falling green clovers over everything EXCEPT snowflakes, as I'd rather go up to grab a snowflake and double back down to get the now-frozen double-point clover near the bottom.
The bonus sections with the large hand at 100, 300 and 800 points really help out--you can see I get from 800 points to 1100 points quickly and with no resistance.
Please ask me to explain anything further in the comments if needed--I'm frequently on TA and will answer all questions related to obtaining this achievement.