Near the place where you obtain the Bronze key, near the stairs (you should notice the Level Infinity Logo), look at one of the corners: there'll be a space you can jump to. Do so to get the secret.
When you're underground, in the water, when you reach the room with a pillar in the middle, move towards the right. You'll eventually drop, indicating that you can dive in this spot. Do so, and when you emerge on the other side, you'll be credited a secret.
After that, when you jump to get the armor, that will count as another secret.
After unlocking the Bronze key door, after you jump the hole, look back and to the left: you should notice a small ledge you can jump to. Jump and follow the ledges and you'll eventually reach an elevator: this place will count as a secret.
(Secret level entrance) From the last secret, ride down the elevator, and when you reach the bottom you'll see the Secret Level Exit.