Successfully complete the game and wait until all the credits complete to see an epilogue sequence.
Kill Guybrush
In the Swamp in Lucre Island, when the other Guybrush gives you the gun, you can shoot him with it. The gun must be one of the first three things he gives you.
Play Pong with Murray
Keep spinning the stool he is on -- to do that try picking him up. When he starts repeating the same warnings to you, face Guybrush the other way and type murryball.
Murray Bites
Change in the tent at the diving contest about 12 to 13 times in a row.
Monkey Kombat moves
While you are on Monkey Island, you have to fight a monkey using Monkey Kombat to get his Bronze Hat. These are the moves you can use and how to use them, as well as which move to use. Note: AA: Anxious Ape; BB: Bobbing Baboon; CC: Charging Chimp; DM: Drunken Monkey; GG: Gimpy Gibbon.
How to do a move
AA to BB or BB to AA: Ack, Chee, Eek
BB to DM or DM to BB: Oop, Eek, Ack
CC to BB or BB to CC: Oop, Ack, Eek
CC to GG or GG to CC: Ack, Oop, Chee
CC to AA or AA to CC: Ack, Chee, Oop
DM to AA or AA to DM: Eek, Ack, Oop
GG to AA or AA to GG: Ack, Oop, Eek
Which move beats another move
AA beats BB
AA beats GG
BB beats CC
BB beats GG
CC beats AA
DM beats AA
GG beats CC
GG beats DM
Frankenstein
Talk to Deadeye Dave about free prosthetic parts until you get a butt, head, liver, foot, stomach, guts, heart, and skin. Combine everything but the skin to make Frankenstein.
Hidden items
While at the school, ring the fire alarm. Mrs. Rivers will run out. Quickly run inside. Look at the treasure chest where you find the whistle. There will be more items inside. Grab one. Mrs. Rivers will catch you and throw you out. Repeat this to get eventually get everything but the wad of tobacco.