The Idol Room
When you enter the idol room during "The Lost Temple" level, don't attempt to cross the red area in front of the idol. If you do, you'll die. Instead, have your assistant Satipo use his shovel to dig up a box. Smash the box to get the parts to build a large fan. Standing on the fan and blowing into the microphone will propel you across to a high ledge above the idol. Now drop down and step on the switch to trigger a cut scene and advance the story.
Bar Fight
During the "Gunfight at the Raven" level, you'll need to fight two waves of bad guys to reach Major Toht, who is inside the room without an access panel on its door. Use Marion to throw bottles at the torches beneath where Toht is standing. Scoring three hits will defeat Toht and advance to the next cut scene.
Cairo Boss
At the end of the "Cairo Street Fight" level, you'll need to beat up a slew of bad guys to make a gun appear. Grab the gun and take aim at the level boss, shooting him until he jumps down and knocks away your gun. Retrieve the weapon and repeat the entire process. After a few more shots, the boss falls dead and the level automatically ends.
Boxer
At the start of the "Rescue the Ark" level, you'll engage in a boss battle with a large boxer. Punching the boxer a couple times causes him to jump up on a tower. Now build an explosive detonator and blow up the tower, causing the boxer to fall to the ground. Punching him will send him scurrying to another tower. Blow that one up in the same fashion. The boxer flees to a third tower, but don't blow this one up. Instead, build a box to jump up on the ledge behind the second tower's previous location. Now build a Whip Pad and use your whip to climb up to the next ledge. Push a box the edge to get the parts to build a fan, which can propel you to another ledge. Build a second fan and float over to an artifact part. Now you can blow up the third tower. The boxer runs next to the airplane. Use the blue bricks from the exploded towers to build a propeller for the plane, killing the boxer once and for all.