Leap over to the right, turn around, make a shield, then super-blast his door. Since you have a shield up, he'll drop some bombs but these will slide harmlessly down the stairs. As they go down the stairs, you'll hear some explosions. After he's dropped four bombs, shoot him. Now run past his rapidly decaying skeleton, stand on the teleporter, turn to face right, then teleport down. Immediately crouch and make two shields to your right. The guard on the right will super-blast the door between you and start revving up another super-blast to take out your shield. Make a super-blast to take out his shield and then shoot him. This may be a close thing so don't waste any time. Now run over to the teleporter on the right and zip down.
You appear in small room with a powerline on the right. Shoot the powerline and teleport back out. Use the other teleporter to teleport up again and then run down the stairs and fall through the hole in the floor made by the bombs. In the underground corridor, run to the right. The next room is pitch dark thanks to that powerline you shot out. Keep running non-stop to the right. You pass over a grating on the floor where the guards shoot blindly up, missing you because of the darkness. As you enter the next room, stop immediately. The light will return and you'll see a hole in the floor that looks like a teleporter but it really just a hole in the floor.
If you drop through the hole, you'll be in a courtyard with several of those huge beasts (like the one that chased you back in the beginning) inside cages where, running to either side would drop you into a pack of guards. Instead of just heading down the hole right away, jump over the hole to the right and pull down the lever sticking out of the right wall. This opens the cages below you as you can hear by the roars of the beasts and screams of the guards. Now drop through the hole and start running to the right. In all the chaos, the guards won't be able to stop you. Keep running to the right and soon you'll reach a long teleporter above you at the end of the hall. Go up the teleporter and then head to the left.
You'll come out just below your friend, still hanging onto that awning. Step up to the edge and you'll release a bridge that your friend can drop down onto. Now follow your friend to the right where you'll ride another teleporter up. At the top of the teleporter, follow your friend down the ramp to the right and into the juggernaut.
As you get situated in the juggernaut, it rolls out into the middle of an arena where thousands of aliens cheer to the slaughter of the alien gladiators. After a few moments, a cutaway view will appear in the upper left corner of the screen. Use the arrows keys to position your hand above a button, which will light up to let you know which button you're pointing at, and the fire button or space bar to hit a button. Some buttons are weapons, some buttons make new buttons appear. Some just turn colors when you press them. Eventually, after hitting the two buttons that turn green and the two buttons that turn red, a long white button will appear. Press it and you and your friend will be shot out of the juggernaut in escape pods.