I would highly suggest to get this achievement before you get the life extensions. The life extensions costs 2k so that would mean you would have to grind another 2k extra.
This achievement will be a grind. I would try to beat the game as far as possible and when you're having a heart time completing the levels with so less life than go back to the first area and grind the star level till you have the 5k. That level gives 10 gold for completion, and you can complete it in a few seconds.