There are 195 levels in this game. If you get 2 stars on every level, you'll have 390 stars. That means you'll need 3 stars on at least 110 levels to get 500 stars, then 2 stars on the other 85.
Obviously, if you can only manage to get one star on some levels then you'll need to get 3 stars on more than 110, but 110 is the absolute bare minimum with the levels that the game currently offers. This will be much easier if you decide to pay for extra power-ups and lives, but it won't be necessary. It'll just take longer if you choose to play through for free.
As mentioned in the other solutions, there are methods you can use to not lose lives (dashboard and quit), but you do risk losing some progress if you do this, as the game doesn't seem to save after every level.
Also, this isn't guaranteed, but there is the possibility that the game will eventually be updated with more levels. If that ever happens, this achievement could become a lot easier. But until then, just remember, 110 levels.
Edit: If you're going to vote negative, I'd appreciate if you'd leave a comment as to why. Since the game randomises the gems, there is literally no way to provide an in-depth guide for the levels. It'll be different for every single person. What I've written is pretty much the only kind of guide you're going to get for this achievement outside of general gameplay tips.