I assume you can play Prince. If you can't it may be a good idea to do some practicing. Level 1 (the normal route) is quite suitable for this purpose. You can find a normal walkthrough through the links-section. When I'm talking about jumping in this document I mean you first have to walk some steps and then jump. You get a lot further this way.
In the second screen you enter, walk right to the screen with the guard. You haven't got a sword yet so you can't get past him. Stand on the left of the screen and get the guard to follow you into the screen on the left. Get him to stand as far as possible to the left. In the screen to the left there's a loose tile in the ceiling. This way you can get past the guard without even touching him, and finish level 1 without the sword.
This is a standard level, although it is the widest level of the game. In the beginning you can jump left twice and pass the guard. Pass the next guard too. Just before the next guard jump at the edge of the screen so you can pass him easily. This also works for the next guy. As soon as you can go to the left, do that. There's a loose tile in the ceiling.
Once you're through the gate (after the giant leap) you can jump three times. Now climb onto the trigger for the gate. Wait a second and then make two running jumps. You jump through the chopper. Now climb back and open the door. When you get back to the chopper, just jump through it and jump again. The skeleton now resurrects. Walk past him, but don't put back your sword. Just keep walking backwards. When you fall, grab onto the ledge (with Shift). Bye bye skeleton!
Very easy. You can jump through the first chopper and walk past the guard without any problems. You'll have to kill the yellow guard. Never mind the second chopper, just walk through it (don't jump). If you didn't know yet: jump through the mirror.
To get past the first guard easily, wait at the left of the plateau. Wait 'till he's real close, and then pass him and stab him twice (he falls). You can easily get past the next three guards. Don't try to get the extra life, you can't.
Walk to the right to trigger the gate. Turn around and jump twice. Stop for a second an walk on (you can jump once). Just walk past the fat guy. At the end of the level, jump.
Walk past the first guy. Watch out for the chopper. Two sections to the right, jump the loose tile from the ceiling. Climb up and directly jump twice to the right. Walk past the guy. If you want to, you can jump once now. Get through the gates, climb down and grab on to the first ledge. Jump twice, walk on and jump again (hang on) and you've passed two more sections. Climb up twice. If you're lucky you can get past the guy (if not, start again). At the end of the level get the green potion and jump down.
You can walk past the first guy, though it's rather difficult. Get to stand real close to him Once you're all the way down just walk through the chopper and keep on jumping (over the spikes of course). Walk past the green guy. In the screen with the purple guy stop right when you enter the screen and then walk past him. When you're between the two choppers you can jump twice. Now jump over the two holes and keep on running (don't jump). Stop at the orange guy and kill him fast. You have to keep two lifes! Jump over the trigger that closes the fence and jump again (grab on). Now jump three times. Open the door and walk back (push the right arrow once). As soon as you're standing still start jumping again (through the gate). Go left and finish the level (this was a tough one).
Go left and jump once. Keep on running and jump again before the choppers. You should be able to get past the blue guy. Kill the next guy you see (into the spikes). On your way back you can jump twice. Go through the gate and go down (!) and left, where you have to drop some loose stones. Get past the purple guy. When you're about to climb down a long way (don't): jump right and grab on just when you're about to splash. For some reason the chopper doesn't work! Get past the last guy too.
Walk past the first guy (watch out for the loose tiles). Now jump twice, but stop while you're on the left of the purple guy. Now walk on with careful steps (Shift+walk), so that the guard keeps facing left. Now climb up, get past the guard and throw him down. The yellow guard is quite easy to kill: wait at the right of the screen 'till you can walk past him. Now stab him into the gate. Open the gate on the left (loose tiles in the ceiling). Trigger the exit door and jump off at the left of the platform. Now you can get past the last guard real quick.
Just before the chopper there's a loose tile. Kick it out and climb up. You can jump twice now, then keep on running. When you're at the right, climb down. When you pushed the purple guy down jump to the right and grab on twice. Walk past the blue guy and push him down. When you get back (after you've opened the gate), jump right over him and get to level 12 quickly.
When you're climbing up at the right side, keep on climbing 'till you can't go any further. Now take one careful step to the left. Turn around and jump up three times. Now climb up and jump to the right. When you meet your shadow put your sword down easily and walk into him. Walk into nothing. You now enter level 12a.
Jump to all screens quickly. When you're in the screen with Jaffar walk on 'till right after the loose tiles. You now fall, so grab on and climb up. You can easily get past Jaffar now. Stab him once (just hammer the arrow up and shift at the same time) and he'll fall. Finished! (Please be careful not to fall as well...)
Time has stopped, so take it easy. Say hello to the princess for us.