The Monkey Island egg is in the Aetherium level. Basically, you must jump into the hole in the middle of the arena (where you later have the showdown with Marduk/Sophia). Jump into the hole and fall through the blue room into the aetherium below, then swim into the tunnel where there is the Palawan portal at the end (I think it is marked with an orange stripe). As you stand in front of the Palawan portal, turn 180 degrees and - voila.
The Close Encounters egg is in Peru where you have climbed the wall in the snake pit and finally do that tricky jump to the place where the big boulder is about to fall down. After it fell to the ground, repeat everything to return there once again, then jump to that ledge where the boulder was. Above there you'll find the egg.