TLDR; Right, Left, Right
Depends if you're going for Time Trial or Multiplayer.
Without the Shortcut
Time Trial - Right, Left, Right because there's no spinies
Because this is the Fast Lap, those horrible spinies that occupy the course aren’t too annoying as the driving line used goes comfortably past/through them. The God Standard here is 26"69 seconds.
From the start, use an Everettstart (Fennerstart) and AB-spin slightly to the left so you drive onto the grass toward the white fence. As you reach the dip in the ground, your turbo start will be wearing off so start a left facing shroomslide and use a shroom. While your kart goes down the hill, hug the fence while building up a MT. When you reach the bridge (or the start of the maze), use the MT and turn left sharply, sticking close to the wall. From here, you should take the right path, either turning or hopping between the rightmost spiny and the wall.
Now for the tricky bit. The following passage happens in the space of about 3 seconds so swift movements are essential
After you pass the corner, go straight into a left facing slide and quickly build a MT around that downhill corner. Let it go as soon as you get it and jump into a right facing slide BEFORE you pass the drop in the road. As you go over the drop stick close to the right wall while building the MT. You should pass by the rightmost spiny here easily. Let the MT go once you pass that spiny and hop over the first bump in the road but stay close to the right wall. Hop over the second bump and when you land go into another right facing slide around the rest of that turn. Build a quick MT here and release it.
At this point, you approach a big u-turn on the track. What is done however is it is cut by jumping across the gap between the roads to your left. This is accepted as a corner-cutter rather than a shortcut.
As you approach the jump, start a left facing slide and build a MT. Release the MT and turn left sharply, then jump off the edge and onto the road below. When you land, straighten and do a MT straight away. Between landing the jump and the big egg, you should put in three MT’s. Try to keep as straight as you can through this part as you lose time by zigzagging. You should pass the giant egg with no hassle and then go onto the bridge. DON’T HIT THE BRIDGE WALLS. That’s just dumb. Just before the end of the bridge start a left facing slide. Once off the bridge, use your second shroom to shroomslide up the grassy hill on the left. You must hold your line here between the cliff edge and left of the single tree. Use your last shroom while holding the slide just after you pass the start of the white fence. Then hold the shroomslide (build an MT to help hold it) and follow the fence as tightly as you can. You will cross the finish line around when your shroom runs out and hopefully, with a very fast time. A good driving line at the end will have you hit the fence at the same time as you cross the line.
Multiplayer - Left, Right, Left
Because of the spinies being in the other route, this is the second fastest.
With the shortcut:
The current fastlap trick was discovered by Martin McMullan.
Drive a normal lap up until the finish line. Do not cross the finish instead go to the left of it. Look for two yellow patches close to each other. You want to sit on the left patch of yellow grass. You might want to play as Yoshi because he makes the next step very easy. Line up the spike on Yoshi's head with the white part of the wall on the far away part of the track. Get close to the hill in front of you and when close hold A and drive down. About two kart lengths before reaching the fence hold your brakes. Jump over the fence (This is hard to do sometimes) and let your kart do the rest. You should trigger a lap and be brought back up near the finish line. You should be really close to the finish because sometimes Lakitu will put you a little bit farther back. You want to be about a kart length away. When he puts you down shroom as fast as possible and if done correctly your lap should be very fast (from almost 7 seconds to just under six seconds)
Reddit (Which has links to video proof)