Koopa Troopa Beach is a mostly easy track with many jumps and a tunnel that lets you skip a part of the track.
Normally, the trick here is to go under the rock overhang, then it all three boost ramps for a chance to get an item like a mushroom or star to help with the cave shortcut. If that does not pan out, you will have to go around the dry sand (get a drift boost here!)
The tunnel shortcut
If you follow the course up until you reach the end of the row of ramps, you will see a narrow ramp that leads up to an opening in the mountain. To make the jump, you must to build up enough speed and hit the ramp straight on (parallel with the ramp), otherwise the if you're going too slow, or jump too far left or right, you will hit the wall and lose time.
The easiest way to make this jump is by using either a Mushroom or a Star while going up the ramp. Alternatively, you can make the jump without an item by jumping with at the tip of the jump. If you are able to make the jump and land inside the opening to the cave, the shortcut cuts off a significant amount portion of the course.
Water path shortcut
If you don't have a Mushroom or Star, there's another shortcut you can use. After starting the course, drive until you reach the first ramp. Veer to your right and drive around the outside of the overhang. You will see a very narrow path that takes you straight across to the other side of the crescent beach. If you decide to take this route, beware of crabs that litter the path.
The giant ramp
At the south east tip of the island is a giant boost ramp that will send you over the top of a rock with a chance to get another item box. Do not chance this jump, as the ramp is thin and it is easy to miss the jump. You will likely see no benefit from accurately making this jump.
Final water path
Before you reach the starting line there are two small ramps and a beach that will have water moving in and out (with crabs walking around, too). Stick to the dry stand unless you have a Mushroom or Star (in which case, cut straight across the wet sand to the finish line).