Super Mario 64 on N64 - The Blue Cap (Vanish Cap)

The blue cap is well hidden: first you need to go downstairs and open the door with the key Bowser left behind in the first Bowser world (Bowser in the Dark World). Then take the underwater passage (on the right) to reach the room with 2 small stone pillars sticking out. Push these pillars down with ground pounds so that they end up underwater. The room then drains of all its water and reveals a door. Go through it to reach the moat, which no longer contains any water. Head to Mario's right to reach a hole that will take you to the blue cap level.

Start by sliding to the left to reach the first platform. Look to Mario's left to spot the platform with the second red coin and jump onto it. Then keep going in the same direction to jump onto the platform with the yellow block. As you can see, the red coin is much lower down in the level, so jump onto the platform right next to it.

If you jumped onto the platform near the yellow block, just slide straight down to the third red coin. As you can see, the fourth red coin is quite far away and you'll need a long jump to reach it. Once you have the fourth coin, finish going down and follow the path to the platforms that go up and down. The fifth coin is quite high up; you'll have to wait until the last moment to grab it by jumping off the sort of giant seesaw.

Let the seesaw tilt for a moment, then quickly run to the other side with a double jump to grab the sixth red coin. On the elevator, turn to the left, crouch and do a backward somersault to get the 7^th red coin, then continue to the right to get to safety. Jump on the big switch to activate all the blue blocks in the world.

Next, go break the blue block and take the cap that comes out of it, run to grab the eighth red coin, then pass through the grate while you're invisible to get the star.