When:
During Part 3, after completing the tasks to unlock the secrets of the map.
Method:
As part of the story, you'll have had to collect six skulls from around Monkey Island and place them onto spikes to the right of the giant monkey head, using them to bash out LeChuck's favourite tune with a bone (!)
Once the sequence is finished and you're...
Reunited with Elaine
Make your way back to the monkey head and retrieve all six skulls from the spikes, then follow the story:
fixing the Sea Monkey using the manual Elaine gave you
After progressing to Part 4, and unlocking that achievement for doing so, you'll unlock this achievement when you gain control of Guybrush again. You MAY have to look at the ship to get it to work - all six skulls should be tied to the hull with rope.