Perhaps you are not sure whether your house is sliding down a hillside or if the hillside is moving (taking your house with it).
When this happens its time to talk to a structural engineer.
There are different causes of foundation movement and different sources of those causes. The issue is whether the past structural movement is severe and whether the house is vulnerable to future movement. If the hillside slope creep is the source of the cause of the movement and the movement is severe, the tieback & underpinning helical pile method is the most economical solution over a retaining wall.
Determining what is the best solution (not just the most economical) requires an engineering assessment and consultation.
Jeremy Livermore, SE, PE
Structural Engineer, License #S5905
Civil Engineer, License #C71491
1133 Camelback St. Unit #11101
Newport Beach, CA 92658