The Secret Aquarium is located in the same room as Jolly Roger Bay, through a hole in the right-side wall.
Three stars are required to access its room without a lobby BLJ.
Tips
Make sure to give full input with the analog stick during each turn so Mario takes tighter, faster curves.
For the first three reds on the floor, line up the top left corner of Mario's hat with the right edge of the pillar to get a good turn.
For the very last red coin, line up the top right corner of Mario's hat with the right edge of the pillar to get a good turn. This allows you to turn earlier, as shown in the video below.
You can reduce lag at the beginning by buffering R, C-Up, and A, and you can reduce lag at the end by using a claw-grip to hold C-Left and C-Up until you grab the star.