By the time you reach the end of the game, you should have alot of coin multiplier gear unlocked. I used all the gear I unlocked and started with a x11 bonus. No need for stressing about this earlier because you will get it later with gear alone.
I found this to be impossible without gear. Save up your coins, and buy some combination of the blue eye, science tentacles, rainbow trail, and butterfly tie. I apologize but I can't remember which exact items are which, but 3 of these items give you a +3 multiplier. Buy all 3, and you'll start off with a 10x multiplier, giving you both this and the 8x multiplier achievement.
As another tip, continue exiting and reloading the program to force new items to appear in the store. Only buy these items when they are on sale. You don't NEED to do this, but it will save you some coins and speed the process up.