It's definitely possible to beat pure nightmare, but it is VERY difficult. Pure nightmare is the hardest mode in the game. You really have to think your way through.
You will be going back and forth between dreams more than in the other modes. Choose your fights carefully. Try to improve your stats, get better weapons and armor as soon as possible. Don't forget that toga lying on the ground right outside Cairo. Leave boosts behind until you really need them, and remember to boost mind before using experience baskets. Use Carrot Transformation only when it gives you more experience than you would get by killing the original monster...
Here's a topic about more strategies used in Pure Nightmare that may get you started on the right track:
viewtopic.php?f=116&t=3587