Sounds harder than it is.
Thankfully, power-ups that you buy also count. So after you get all the upgrades and skins that you need for achievement, spend all your coins on this buying and using this one. It's the most useful powerup anyway.
Some tips for farming coins:
Use the widest and shortest basket skin you have. This makes catching stuff at the last possible time easier.
Prioritize coin drops over stars. Just be sure that you don't loose the game before actually catching the coins.
As coins drop slowly, it takes 2-3 stars to drop before coin gets to a level where it can be picked, so no need to panic right after it appears.
Don't forget that for every five ice you bump with side of your basket you get 5 coins. This is the most reliable and constant way to get coin. More Ice "debuff" is actually usefull for this, as long as you accidentally don't catch the ice.
The power-up counts towards the achievement right when it is used, so there's no need to wait for it to run up.
You should be gettin around 200-400 coins per five minutes, depending on the RNG.
Either this or the 5000 points achievement will be the last one you'll unlock.