After getting past crushers on conveyor belts and making ample use of bombs, the vikings must jump their way to the exit.
Reach the Exit
Have Baleog and Olaf stand on the lower part of the see-saw, and have Erik jump on the higher part. Olaf should go up first, raising his shield to try to avoid the flying robot attacks. He should pick up the Omega Bomb, but I recommend not using it until Olaf reaches the top, where there is a second flying robot. Use the Omega Bomb here to kill the flying robot at the top, then use the red key on the keyhole. Olaf can reach the ledge by first jumping on the highest spring, then falling down to the second highest spring and jumping up from there. He has to fall onto that second spring from higher up so that he will have enough momentum.
Have Baleog come up the same way, trying to avoid that flying robot in the middle as he goes. Finally, Erik can jump up to the lowest spring if he runs toward it. Just be sure to hold the jump button until he's on that spring. Then he can come up, get the tomato at the top by holding the jump button, then join the other two vikings.
Send Olaf to the right with his shield raised so he can cross the conveyor belts without getting crushed. Have Olaf float off of the right side, down the pit until he reaches a crane. Then have Baleog go down the elevator and shoot the chain to make the beam fall. Next, Olaf should operate the crane, dropping the beam through the hole that has a laser over it.
Next, Erik should go to the right, jumping over the spiked pit, and go right along the second conveyor belt as well. Then he should go to the right and fall down the hole, where he will land on a spring. Have him land on the ledge, then carefully jump up along the conveyor belts. There are collapsing bricks above the lasers, so be sure to jump off of them as soon as possible. Carefully avoid the flying robot at the top, then fall into the hole on the right to get the blue key and land on a spring below. Then have Erik get up on the ledge and go down to the blue keyhole to unlock the exit.
After that, Erik should go to the left and operate the crane to put the beam into the gap with the laser in it. After that, Baleog can ride the elevator down if he hasn't already, and he can go to the right and climb the ladder to shoot the button on the right. This will open a hole that Olaf can come down to join the other vikings. Then all three vikings can go to the right to reach the exit.