Repairing or replacing a concrete retaining wall
If the wall is standing straight and the trouble is a clogged drain or water pooling above it, clearing the drainage and fixing the grade can be enough. A wall that's tipping forward or pushed out in the middle usually has a problem in its footing, steel or drainage that a patch won't reach, and that's when I'd replace it with one designed for the site. I'll tell you which one I see once I've looked behind it.
What shapes the cost of a concrete retaining wall
Height and length set how much concrete goes in, but the design sets the rest, from how deep and wide the footing is to how much steel and drainage the wall gets. A tight backyard a concrete truck can't reach costs more to pour than an open slope by the street. If the budget is tight, I'd trim the finish before the drainage, because you can't see the gravel and outlets once the wall is backfilled, and the wall's life depends on them.