I agree with Kent about the controlls, if you are using unity, take a look on your animation transitions, maybe take off the transition time.
Also, need to take a look at physics, it maybe worth to try to change the constraints in the rigidbody.
Maybe make the moving platforms one sided colisions, because 2d moving platforms generally can be jumped to from downside, a lot of people with hit the head and fall for the spikes expecting that.. not me tho *blinks