Leaning timber retaining wall
That is not unusual in our neighborhood. A sledge will do nothing but break wood. Repairs that have worked are to dig out soil behind the tipped area and replace the vertical posts with longer ( deeper) ones. The larger the concrete "footing" for the vertical posts , the more resistance to tipping. Additional support can be added by driving metal bars into the ground a few feet behind the wall and attach these with steel cables to the vertical posts. The bars and cables will be under the ground surface so not seen , Yes, they will corrode in a few years but by then the soil will have settled down and be stable ( hopefully). I did this with 3/8" steel cable and it was still holding when I moved 5 years later. The digging sounds worse than it is , or contract it.You only need to remove a narrow trench like 2 ft wide and not necessarily all the way to the bottom. An Auger would be a help. I have also seen a new stronger wall built where boundaries permit ; then fill in the narrow gap between the original wall and new wall .