Quick answer: To get past the Garfield: Escape from Monday Sugar Seas jelly crocodile, dive deeper, wake it, and hold on. After it drops Garfield, follow it until you can jump onto it and hold on again for the ride toward the surface. Source
Players also call it Sugar Seas jelly crocodile or Sugar Seas surface route.
How to use the jelly crocodile to reach the surface
Dive deeper and grab on
Go deeper into Sugar Seas, wake the giant jelly crocodile, and hold on to it. Source
Follow it after the drop
When the crocodile drops Garfield, keep following it and survive the route until you find it again. Source
Jump on and hold on again
Jump onto the crocodile when you reach it, then hold on for the ride back up. Source

Getting dropped does not finish the route. Follow the crocodile and grab on a second time. Source
FAQ
Dive deeper, wake it, and hold on. After it drops Garfield, follow it, jump back on, and hold on again. Source
Use the jelly crocodile twice: grab it below the surface, then follow and remount it after the drop. Source
Wake the crocodile in the depths, hold on, follow it after the drop, then jump on and hold on again. Source
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