One of the most difficult aspects of hitting a side hill lie is keeping your balance through impact. This is especially true when the hill you are dealing with is very severe. Most people start losing their balance prior to impact on these shots, thus causing a terrible mishit.
The remedy for this is what I call “Forward Foot Down The Slope.”
The procedure you go through for this is to get your body and club aligned as if you are hitting a straight shot. Then you move your forward foot down the slope and move your back foot up the slope. This makes the stance closed for when the ball is below your feet and open for when the ball is above your feet. The more severe the slope the more closed or open the stance should be. Personally, I alter my knee flex to get my hips square to my original alignment. When you swing with this set up you should be able to maintain your balance through impact and hit the ball more solid and with more consistency.
On side hill lies the ball tends to jump or curve off the line due to the angle that the club plays through the impact. If the ball is above your feet it plays too upright. The ball tends to pull and hook because your feet are too flat. If the ball is below your feet it tends to punch or slice.
For the ball above your feet you can take more club and open the leading edge to get the face of the cub pointing where you are aiming. This should take the pull and hook tendencies away. You use more club because opening the leading edge adds loft, and the ball will go a shorter distance. The opposite procedure is done with the ball below your feet because it takes less club, and closes the leading edge, again getting the face to point towards the target.