What is a good stabilizer for Y axis?
A 3-axis gimbal can reduce rotation but not translation - ie it will twist in 3 axis to smooth the motion, but it can't physically move to account for your movement up and down.

I think there are three ways to resolve this: 

Use a body mounted stabiliser that compensates for movement.  These are expensive and cumbersome, but they work. They also reduce arm strain as the weight of the camera is taken by the body straps.

Practice compensating for the movement yourself. The best way to imagine this is to move as though you were carrying a hot drink instead of a camera. This is free, but requires some time to practice.

Shoot at a higher resolution than you need to deliver, then use digital stabilisation to try and improve your video.  This works to some extent, but any motion blur due to camera movement will still be visible, depending on the shutter &amp; frame rate you shoot at.