Highlight the white text inside the block for hints ranging from vague to specific...
Note the size of the grid: 25x25
You can quickly eliminate certain paths by remembering that you must continue from the corresponding part of the paired island and in the same direction. For example, entering the 9 of Spades island on the spades symbol instantly teleports you to the spade symbol on the other island (don't count it as another movement) continuing in the same direction.
A segment of travel never ends on an island.
No path ever crosses an existing path, so once you have drawn one segment, you may never cross it again.
Note the 24 length segment. It must go from one side of the grid to another while never crossing an island. There are few places where this fits on the maze, so try from this point to the end. That will constrain other paths.
The 26 length segment crosses the 10 of Spades
The first island is the 4 of spades.
The last island is the J of spades.
The third island is the 5 of spades.
4, 2, 5, 3, 8, ..., J. The rest is left as an exercise for the solver... :D