I'm trying to make a polygon type hair, which moves as naturally as in the first gif, but it doesn't see like it and it doesn't stay in its place, (I used the softbody for the hair anyway) is there a way to get a more natural movement?
There is something wrong with how you weight painted the mesh. If I remember correctly, if you weight painted it at "the roots", the part of the mesh that is not weight painted should move. Or it could be the other way around. So just to be sure, here are some videos to help you out on the softbodies issue.
Hopefully, these videos can lead you into the right direction.