How big are your animations (images, number of frames)
It sounds like you're just using an unrealistic number and size of frames to get a good frame rate. However, once the Spriter plug-in is ready for Construct, this will help people avoid this issue. :) But you'd have to recreate your animations with Spriter...
Well, the shakiness comes from the collision polygon. A runner type of game is like a platformer. It is advised to have an invisible sprite of square/rectangle shape with the platform behavior on which you pin or position each tick the sprite with the animations. But the collision polygon of the anim doesn't count, only the "support" sprite does.
Also your project was missing the 'Set animation "running"' action. You also should set the "Default controls" property of the platform behavior to no. You also should set the option "Loop" of the running animation to yes.
Also you don't need the touch2 plugin, the built-in touch allow you to use either touch and mouse input. Prefer using built-in than custom plugins.
Using a support sprite, and making sure the origin points are consistent from a frame to another should help with the shakiness.