It's not clear from your gifs which object is Sprite and which is the Character?
Is the movement smooth if you disable Physics behavior?
You should avoid changing x,y position for Physics objects, directly or with other behaviors like Bullet, Sine etc.
Ideally physics objects should only be moved using Physics actions like Apply Force, Apply Impulse, Set Velocity etc.
See this demo for example - the ball is moved to mouse position using impulses (last 3 events):
https://www.dropbox.com/s/9cdcj8omeurgs ... .capx?dl=0
Also, to ensure consistent movement on different framerates, use lerp with dt:
lerp(Self.X,Sprite.X, dt*10)