Enable bullet mode on main character in order to get rid of the ground stutter and tunneling.

"By default, Box2D uses continuous collision detection (CCD) to prevent dynamic bodies from tunneling through static bodies. This is done by sweeping shapes from their old position to their new positions. The engine looks for new collisions during the sweep and computes the time of impact (TOI) for these collisions. Bodies are moved to their first TOI and then halted for the remainder of the time step.

Normally CCD is not used between dynamic bodies. This is done to keep performance reasonable. In some game scenarios you need dynamic bodies to use CCD. For example, you may want to shoot a high speed bullet at a stack of dynamic bricks. Without CCD, the bullet might tunnel through the bricks."