This is a lot simpler than you may think. I unlocked this achievement without too much trouble.
Advice:
• Take your time with jumps, attacking enemies, and spikes.
• Don't get greedy. If there is too much in the way for a solitary gem, it's not worth it.
• Spawn the Blood Ghost. It's easy to defeat, and will offer up some bonus gems in a purple chest.
• Use the magic glasses to find the hidden gems.
• If you find the hidden door in World 1 to Flamy's room, you can get some bonus gems here.
• Spend as little as possible in the shop, as I'm not sure if you need 1000 all at once.
Hope this helps you out. If the guide needs adjustment, then please leave a comment. Corrections or additions welcome.