Guide status: INCOMPLETE
So I'm writing this guide as I go through this game for the first time. I'm by no means an experienced Out of This World player, so this probably won't be the de-facto guide for the game, but if it worked for me, it should work for you, too. If I haven't covered a section, I haven't beaten it yet. I don't know if the other versions of this game, also called Another World, go much differently, but just in case, this guide is for the Super NES version of the game, which is how I'm playing it.
In this game, you take control of one Lester Knight Chaykin, who's suddenly transported to a strange, alien world after committing a cardinal sin of science: performing complex experiments during a thunderstorm. It's up to you to keep him alive and lead him through this bizarre landscape which hopefully, somehow or another, leads home.
D-pad - move
Y/A button while standing - attack
Y/A button held while walking - run
B button - jump
Start button - pause
Pretty standard stuff...
You start out taking an involuntary bath when your desk is zapped into a pool of water. Press and hold up to swim to the surface.
Don't stand around by the pool too long, or a tentacle will emerge from the water and drag you back under. Proceed to the right, stopping to kick the little leech things. They take one hit to kill—but so do you, so be careful. I recommend approaching them walking rather than running, then mashing the kick button once you get close. You should take all of them out so that they don't get in your way when you're running back through these screens in just a moment.
After going right for a few screens, a big beast with big fangs will drop down and give chase. You're not kicking your way out of this one, so just run back the way you came. It'll almost catch you, but don't freak out, as it'll trip. Keep running until you're on the screen to the left of the pool and you come to a ledge. Jump off the ledge to the vine, and you'll swing behind the beast. Now, keep running back to the right to finish the first section.
Once you've run far enough, a cutscene will play, wherein a cloaked figure will walk in and shoot the monster that was chasing you. Don't get too cozy, though... You're next.
You'll come to in a cage hanging over a pit with an alien that looks kinda like Marvel's Thing for a cell mate. Don't worry about him though, he's friendly. Move the D-pad left and right to swing the cage, which will fall on one of the guys who shot you, which is also a Thing. You'll both exit the cage, which broke open after the fall, and you'll need to crouch down to pick up the deceased guard's gun.
The gun has 3 abilities. Tap Y quickly to fire a laser. This replaces your wimpy kick. Hold the button for about a second to set up a barrier. Hold the button for several seconds to charge a powerful charge shot, which can shoot through barriers and even some solid walls. You'll need to use all these abilities very soon, so be sure to get comfortable with your other new best friend.
Run to the right, blasting any guards who get in your way. One regular laser should fry them. Make sure to keep your friend alive, too. Your lasers won't hurt him, but the enemies will. Keep going until you hit a wall, where your new pal will fiddle with something on the wall until it opens. Don't bother fighting (did I mention you have limited ammo?), just keep setting up shields to protect your partner in crime until he gets the door open and the both of you can make a break for it.
Once you're on the elevator, use the D-pad to go up to the top floor, where you can go to the window to your right to see a cinematic shot of the alien city you've ended up in. I don't think this is required, but it looks cool. Now make your way to the bottom floor.
I had a lot of trouble with this part. You have to blast the guy in front of you the split-second you enter the room to your left, or else he'll blast you first. Just slowly walk onto the screen and as soon as it changes, shoot. The timing is tight, but I believe in you. With that guy out of the picture, you'll have to shoot a little flashing button on the wall. If you don't see it, you probably already shot it during the firefight. The screen will flash white when you hit it.
Now you can take the elevator one floor back up and go to the left. You'll be above a guy in a room behind three closed doors. Use a charge shot to blast through the locked door in front of you. The guard will hear you, but that button you shot on the floor below locked his doors, so you have time to run before he shoots through all three.
Press down on the D-pad to warp through the open part of the floor and run to the left. Similarly, press up to warp up through the open part of the ceiling. After that, you'll hit a closed door with another guard behind it. Your friend will open up a manhole so you can escape into the pipes. Jump in and roll down off the screen.
You'll drop down into a dark pipe maze, rolling on your side as you search for the exit. Start by going left. You can't see far in any direction, so don't go too fast.
You'll soon come across a break in the pipe letting hot steam in, a burst of which will take you out. The timing is a little tight, but if you lightly tap the D-pad, you'll just inch forward instead of doing a full roll. Use that technique to get as close as you can, then as soon as the steam stops, roll through.
Continue rolling until you fall down to the next section, where you'll run into more steam. Be patient and go slow so it doesn't jumpscare you like it just did to me.
After rolling off another ledge, you'll be at a fork in the road. Go right, again avoiding the steam, then go left, then go right until you fall off the screen.
You'll land in a blue room, facing a door that will open automatically. Walk inside it to recieve a zap that will reload your gun, which you should then use to blast open the walls to your right.
After running through a hallway, you'll come out into an outdoors area with a guard who can't see you yet. Try to shoot him before he can. You'll also see your buddy running by in the foreground, escaping more guards, who are shooting at him mercilessly.
You'll come to a cliff. You can't jump across, but you should still jump. You'll land on another ledge below, where you can shoot a hole in the wall to your right with a charged shot. Do so and head in.
You'll be inside a system of caves. Walk into the hole to your right, then hop over the pit and keep running right, hopping over the pit falls as you go.