Load the game through the DOS prompt, using the command:
PRINCE MEGAHIT (older versions)
PRINCE IMPROVED (newer versions)
This will activate a cheat mode:

Start the game by typing 'prince megahit X' where X is a number between 2 and 14. In addition to getting access to the cheat codes the 'megahit' switch normally gives you (as listed on GameSages and GameWinners), you will start the game on level 2-14 depending on the number you chose. 13 corresponds with the second part of level 12 (where you get to fight Jaffar), and 14 corresponds with the final few rooms after Jaffar's defeat. Entering 15 or above, or anything other than a number, will simply make you start in level 1.

Rather than take the long way around to find the sword and then beat the door guard, go down and right from your starting position, wait for the guard to approach, then run left just before he is within striking range. You should be able to lure him with you into the next room. Run all the way left and climb up just before he comes within range again. Go left, probe the ceiling in the next room for a hidden passage, go up and then right again to return to the starting room. From here, go down (you'll end up to the right of the guard), and quickly dash right toward the exit. You'll be able to finish the level without ever fighting the guard, and from level 2 onwards you'll automatically be given the sword even though you never collected it.