So, this is the worst part of any run... ever. I hate this puzzle, and you will too while you're running this game. So... here's a walkthrough to save you the pain:

[Before you start, dock 3 and 4] Then start in (2) [Docked will be indicated by ^]

TOP | BOTTOM 2 > 4 | 2 > 3 3^ > 2^ | 1 > 2^ 1 > 3^ | 3 > 1^ 2^ > 1^ | 4 > 1 4 > 1 | 2^ > 4^ 4^ > 2^ | 1 > 3 1 > 4^ | 1^ > 2^ -------- 3 > 1^