Here's how to get a gun in Shadow of the Beast (I found this out by experimenting in desperation). Right at the start point, the character operating the canon (next to the well) has a gun. To get it, stand just to the left of the canon, wait until he lights the fuse on the canon, and then punch the canon. It will flip to the right, and kill him with the ball (It will also kill the big monster just to the right of the start point). A gun will appear where the canon operator was.
Let me know if you have any tips. I always need them. :)
Outside. Start by running to the left. Watch for the bats that will fly down (I've only made it through here unscathed a couple times, normally I just run back to the right a little bit and duck when I hear the bats shriek). There are two different sets of bats, and each set of bats will attack in two different smaller groups. As soon as you get past the second set of bats, there are three metal traps in the ground. All you need to do is jump and land between the sets of "jaws". Enter the tree (there is nothing of value further to the left).
In the tree, part one. The small head at the bottom of the staircase will shoot at you when you get a certain distance from it (something you're bound to discover on your own!). Climb down the ladder and head to the left. The game progresses pretty linearly here. You've got a few platforms to jump and a few monsters to dispose of, but there's really only one way to go. When you get past the green guys with the swords (watch out for those spikes overhead!), climb up the ladder and head to the right (passing the next ladder which is heading up) until you come to the ladder that goes down. A bit more jumping on platforms and you'll come to a blue total health restoring potion. Things progress a bit more and you will encounter these golden flying things. When you are at this point, you will climb down a ladder and find a silvery (but with red center) circular device stuffed in a corner to the right (somewhat near a big skeleton lodged in the wall). This is a teleporter that will take you back a ways. Don't use it yet. Instead, head to the left, ignoring the ladder heading down.
Next, you will come to the weird eagle thing that is holding a blue crystal globe. Time his fire-breathing activities and get up close to him when he's not scorching the air in your vicinity. Ducking will avoid the fire. Then, when he's not breathing fire, punch the globe (it will flash each time you hit it). I counted eleven hits for it to be finished. You will then have the blue globe in your inventory (you'll get to use it soon enough). Head back to the right the way you came, and then take the ladder down.
You will climb down a jog in the ladders, and then head left instead of down. To the left, you will find an area with a key. I've found it easiest to jump off of the moving platform into that section and then getting onto the up-down moving platform without the resident blue guy seeing me. (Basically don't walk to the left at all after jumping off of that moving platform. Just hop straight onto the up-down platform). Now, head back to the right. If you need health, climb down that ladder that I told you not to climb down before and head to the left. All the way left is a blue complete health restoration potion.
I have a hint for this whole section. I found it much quicker to avoid catching all the ropes and jumping on all the platforms by simply falling off the ledges. The health potions were conveniently spaced so that I could easily survive these falls (watch out for spikes though!) and leave this area with full health. Climb back up the ladders and hop in the teleporter.
After teleporting, hit option 1 and select the blue globe. The blue globe gives you a nifty missile weapon. Head left and climb up the ladder. When you move to the right, a wall will rise sealing you from escape! There is a lone spike "bush" in the middle of this little battlefield. Stand with the Beast's right foot just about touching the left edge of the bush. When the monster rises up, duck. You should be below his shots. Note that before he rises up, he will fire one shot. Try to jump over them, but they don't do too much damage so don't worry too much. I comfortably get four shots in before I have to duck. It takes fifteen shots total (don't waste these shots, I've found them useful later). Hit option 1 and select "exit" in order to go back to regular punches. Off to the right, you enter the second half of the tree and a new save point!
In the tree, part two. As you run to the right, you will run past a machine with a lever, gears and a chain coming out of the top. Ignore that for the moment, and jump over the spikes. After you climb down the ladder, there will be some snakes coming out of the floor and spitting at you. Just run up to them and punch them after they spit. After the second and third snakes a bird thing will fly down and you will need to duck. Don't take the downward ladder after the snakes. Instead, pick up the gear and head back to the machine. Once there, hit option 1 and select the gear. Assuming you're standing close to the machine, the gear will go in place. Punch the lever and a platform will lower. Climb onto the platform and punch the lever again to go up. Go to the right and get the torch hanging from a support pole. Head left, beat up some green guys and flip the switch on the wall. Climb up the ladder you past when you went to flip the switch, and head left past the bouncing eyeballs (!?). When the dragon stops breathing fire, run, pick up the key and stand next to him and wait out his next attack. After that, run back to the right and past the eyeballs. If you need health, head to the right and pick up the blue potion. Otherwise, head back down the ladder and the "elevator". Go past the snakes again, and then head downward. Head right and punch the lever. Then turn back and cross the platform that had been extended across what used to be a gap. Punch the lever you find off to the left and then go back to the right and downard (gadzooks! They've got you running back and forth!). Run left after getting to the bottom of the ladder and use the moving platforms to take you further left. You will find a blue "glove" suspended in midair. If it's surrounded by electricity, you forgot to flip the switch in the hallway underneath those bouncing eyeballs. As you head back right past the ladder, a couple of those red batlike things will fly down. Try to hit them, because now is a good time to conserve health. You've got a ways to go before a refill. Continue on downward and avoid the obstacles (I have really got much to comment on here. Just practice your timing around the spikes and try not to get hit.) When you get to the ghosts, if you head right instead of down the ladder to the left you can avoid having to deal with these rocket engines that are mysteriously igniting. However, only avoid those engines if you have the health to take a fall into spikes (and you must also be confident of your ability to get rid of the dragon). Hit option 1 and select the yellow glove. You can't kill the dragon without it. If you watch the timing, you will notice that the spike will drop to the floor and the dragon will stop breathing fire. That is when you need to jump across. You can comfortably punch the dragon five times before you need to jump back across when the spike is down. It takes a total of thirty hits to blast this guy. Use the yellow key you picked up to leave the tree area through the well.
Topside once again. All right! So we're out of that hellhole of a tree. Well, there's still a bunch of ickyness to deal with up top. First, stand in front of the cannon. After the nifty little green dude lights the fuse (wait for it to be burning), punch the cannon. The little guy gets blast and leaves a handy gun behind. Now, head back to the right eliminating the baddies that you encounter. The columns that look like piles of rock contain potentially useful items (there is only one evil column in the game, and that comes near the end). The first two you come across have health bonuses. The last one contains a large ball. Push the ball along with you as you avoid the spikes and use it to plug up a hole from which some green and red balls are popping. When you get to the funky pterodactyl statue, don't be alarmed. This is actually a pretty easy monster. He does a bit of damage if he hits you, so don't let him. Punch the statue five times to let the monster out, and then punch him three times to take back the freedom you just gave him. I personally hate the spider forest that comes next, but at least there is health afterwards. To get past each spider, wait until the spike on the right has just come down, and walk over until you are directly to the left of the spider. Punch the spider, wait until just before it hits the ground, and jump into the air. Let the spider go under you, and move slightly to the right to land where the spider had been, between the spikes. Wait until the spike on the right has just come down, and walk to the right. The second time you repeat this process there will be a spider running along the ground which you must jump over. The eyeballs aren't too bad once you see the holes that you can rest in. Duck as the green guy flies overhead, and then punch him as he comes back around but lower. When the flying dragon drops the winged bomb, punch the bomb before it explodes and it will eradicate the annoying swarm of insects. I think you can handle the rest of the obstacles until you get to the castle.
In the castle. Go left, past the ladder, and get rid of the green, hoppy guys. Flip the switch. Go back and climb the ladder. You can only punch wooden barrels; the silver balls and indestructible. There are two wooden barrels followed by a metal ball, and this repeats itself indefinitely. Hit the first wooden barrel, and use the ladder up to the next level as a means to dodge the second barrel and the metal ball. When you get to the floor where the barrels are dropping down, run to the left and flip the switch. Climb the ladder to the top floor, and punch the chests to the right for health, except be forewarned that the very last chest contains a green guy who shoots arrows, and the second to last chest can be stood on to avoid the arrows. Kill the green guy by punching the chest before getting the last bit of health. Run to the right, avoid axes and flying dragons. Pick up the wrench. Climb down the first ladder you come to. As you run to the right, watch for green dudes in the floor which throw knives at you. To avoid getting hit by the axes that come down, stand right underneath whence they come, and they'll fly over you from each side. After defeating the three big green mouths, run and jump across the gap. You need to jump at the last second to make it. Punch the little head in the wall three times, and jump onto the chandelier as it lowers. Wait for the spider to go up to run underneath it. More axes. Some spiders need to be punched once or twice before they'll go up. After climbing down the ladders, you'll be back near the entrance. Go right. You might want to consider using some of your remaining shots from the blue ball to kill the red bouncy blobs and the bats after them. The gates here will only be open if you've flipped both switches prior to getting here. Climb down the ladder; don't go all the way to the left. Some health is on the right then. Go left, wait for the metal ball to pass, go left, climb the ladder, climb into the pit, and duck. Wait for the ball, go left, and climb down the ladder. Pick up the spare bullets, and climb down the next ladder. Run to the right until you see the gargoyles; then run back to the left, and punch the button on the wall. There's another green guy in the floor after the axes. Use the wrench to get past the electric field. Climb up the ladder, go to the left, and flip the switch. Arm yourself with the gun, climb down the other ladder, and go to the right. Get in close, and just shoot. And keep shooting. You shouldn't need to refill the gun. Use the blue key to unlock the door. You are now outside.
Outside the castle. Go right. Punch the tombstones for health. In the second set of tombstones, the second tombstone contains a ghost instead of health. Kill everything. To kill the final guy, watch his shot pattern. Get in close and jump and kick the face in the middle of his body. Congratulations, you won.