The Alligator is an animal that appears in Crysis 3 as an easter egg.
The alligator can be found in the level The Root of All Evil . After you blow up the dam and just before you encounter the guards you will find a pipe with fish on it. If you press it an alligator will swim out of the pipe. Then you can jump on it and ride on alligator pass the guards which will ignore (unless you shoot). After swimming through the river the alligator will just dissappear.