This guide shows you how to get all 3 gems.
How to Get All Gems
The ruby is in the Mushroom Forest near the Forest Spirit. You need to find all 7 mushrooms in the area then talk to the spirit to open up a new path. Talk to the thin mushroom at the end of the path to start a fight. The mushroom will give you the ruby at the end of it.
The aquamarine is also found in the Mushroom Forest. Go to the first area and walk to the left side. There’s a door that can be unlocked with the golden key you get from the Brown Mage. Follow the path on the other side of the door and interact with the jump rope to start another fight. After the fight ends a new path opens up with another door at the end that requires the stolen arm to open. The aquamarine will be in the middle of the next room.
The emerald is found inside the chest in the shop at Midnight Town. Just like the locked door, you can unlock the chest with the golden key. Opening the chest starts a fight with the Light Being. You have to kill the Light Being before the fight ends, if you don’t kill it, you’ll need to reload your save to try again. Once you kill it, the emerald can be picked up.
The statue is in the Cosmic Hub, I have no idea what makes it show up but it seems to be random. Leaving the hub and coming back to it repeatedly should work. Interacting with it will allow you to insert every gem inside it, starting one more fight.