All the answers on this page is acceptable, but it is important to remember that by this point in the game you ought to have enchanted your sword. While it is not necessary to do so, it does make this level reasonably easy to beat. However, each sword requires its own technique.
With the Sword of Flames, the extra damage makes it rather quick to finish off opponents. On hard mode with a level 5 sword, I found that I kill all the enemies before the asterisk can hit me. The technique here is to watch your health, drink potions when your health drops low enough. If you are teleported to the beginning, drink a potion so that the countdown timer will run out by the time you reach your next opponent.
With the Sword of Life, I found that on regular mode your life will not drop to the point where you will die. The technique is to weather it out and collect candies (though I found this method of earning money rather slow in the long run, especially when you have the GMOOH potion to get to the cow level). After some time, enemies will stop spawning altogether.
If your health isn't high enough or your sword doesn't heal enough, you can use the health potions to prolong your life, however, this can be costly your fist time around. With this said, the technique most people use is the berserk potion. 5 of them are given to you by the frog for answering his questions. The problem is to once again watch your life. Couple the berserk potion with a healing potion or a fire scroll to minimize your chances of dying.
I should also offer you this caveat, this is the level you receive the armor which will reduce the damage you take. There are only a handful of items in this game, so you don't want to miss an item. If you are in a rush to beat the level, your opponents might not drop the item. I suggest that you first tank the game with potions and teleports until you collect the armor, then try the techniques mentioned above to beat the level.
Finally, I have avoided the Sword of Summoning because I have yet to play with it. However, referencing LessPop_MoreFizz's answer, the summons from fallen enemies help to extend your life and allow you more time to heal. Using berserk potions (assuming you have not yet used them all) seems to be the easiest method to beating the level regardless of which sword you use. However, if you rush through the level, once again, you risk missing the armor. I would use the same techniques used with the sword of life with the sword of summoning. Perhaps coupling the flame scroll with the berserk potion would be the easiest method to beating this level.