Unlock Gallery Art
Each time you finish a level, concept art for the level in question will be unlocked for viewing by accessing the Extras menu.
Unlock Arcade Levels
Finish levels in story mode to unlock them for Arcade play.
Defeating Eldridge
Wait until he is walking toward a barrel and gets close to it. Then, shoot the barrel and it will explode, flipping him over. Start shooting him after he flips over. Later in the fight, he will start charging you. When this happens, run along the walls until he runs into one, then start shooting him.
Defeating Nathaniel Payne
Use your shovel like a baseball bat. Hold X and release when he throws a chunk of rock at you. Do not get the rock confused with the energy ball that is thrown.
Defeating Trisha
When she opens her mouth, throw a piece of dynamite into it.
Crystal order at the museum
The order to insert the crystals is red, yellow, blue, green.