If you have problems with "deadzone" of Xbox 360 Controller, you can use d-pad.
In the launcher of the game select "Input" tab. Configure your gamepad. Something like this:

HORIZONTAL (+) d
HORIZONTAL (-) a
VERTICAL (+) w
VERTICAL (-) s
HORIZONTAL (+) Joystick 1 axis 5 (press d-pad arrow)
HORIZONTAL (-) Joystick 1 axis 5 (press d-pad arrow)
VERTICAL (+) Joystick 1 axis 6 (press d-pad arrow)
VERTICAL (-) Joystick 1 axis 6 (press d-pad arrow)
Pause escape Joystick 1 button 6
Jump space Joystick 1 button 0

You may also want to invert y-axis. You can do it in the pause menu.

[Tested on 52A-00005]