This Seeking Tech guide will explain the best post-game method when it comes to farming coins in Astro Bot.
Use the following video as a reference:
For the first step, make sure you beat the main campaign. This will unlock the Deja Vu Dimensions, which is where you can replay the Credits Clash stage.
For this level, you will get a coin for every letter you destroy. If you destroy the connected letters, then you will get bonus coins. With that said, you should only try to destroy the easy ones that are directly in front of you.
The memory cards will also give you coins when you move past them.
When you get the frog power up, use a spin attack and then extend your arms outwards to quickly destroy the letters.
Once you get to the gatling gun, make sure you destroy all the letters before moving on to get the bonus coins.
When you get the bear powerup, you should also make sure to destroy all the letters.
Once you get to the top of the wall leading to the PS1, you can restart or leave the planet.
I was able to get more than 950 coins in around 4 and a half minutes using this method.