After evolving your first (Adventurer) monster at level 18 using 20,000 coins, you will unlock double jump. This will allow you to go above the level and collect the gold coins worth 5 each.
Once you have double jump unlocked, save 8000 coins and purchase the special item that doubles the value of your coins. This will make your silver coins worth 2 and your gold coins worth 10.
If you attack lots of monsters you'll go into frenzy mode, making all of the silver coins into gold for a limited time. This only happens for the Adventurer.
Start at level one and play through without stopping. You should earn your 2,000 coins part way through the third level if you haven't died, I was able to earn slightly over 4000 coins on my run.