In order to earn gatcha prizes, you must go to the Gatcha Prize Machine, which is located in the back of the PlayStation Labo. Gatcha prizes can be obtained by spending PS coins. One gatcha prize will cost you 100 PS coins. In total, the Gatcha Prize Machine offers you 60 prizes to collect. This will lead you to have to spend a total of 6,000 coins on the Gatcha Prize Machine. This may sound like a lot of coins, but 6,000 PS coins can actually be earned fairly quick.
The best way to earn PS coins fast is to play each level at least 2 or 3 times. Coins are always sitting on the paths you need to take, so pick them up whenever you see them. It's also important to know that coins can be collected from defeating enemies. Each enemy usually drops about 3-5 coins. So each time you're in a level, just make sure to pick up coins lying around and defeat as many enemies as possible. Once you collect 6,000 PS coins, go spend them all at the Gatcha Prize Machine, and you'll unlock the trophy.