Crysis is a still considered a very demanding game despite it's age. The Radeon HD 6670 is a good budget oriented graphics card. However, I think you are simply asking too much from it.
The easiest thing to do is to replace it with a more powerful graphics card. Or you can lower the resolution. See following review of current generation $90 - $150 graphic cards for benchmarks of the Radeon HD 6670 which generally use the highest settings or "ultra".http://www.techpowerup.com/reviews/HIS/HD_7750_IceQ_X/10.html
Note that the benchmarks includes graphic cards that are far more expensive than $150. The GTX 690 is probably around $800+