How can I remove a retaining wall made of vertical landscape timber?
If they are vertically embedded in the soil, and if you can get heavy chains wrapped around them individually, you might be able to lift with something like the bucket of a backhoe or a loader.

Alternatively, you can remove the soil around them with a backhoe or even with hand tools. In either case, you're likely to have to pry them apart. Landscape timbers in a retaining wall are often held together with embedded pieces of rebar. When I removed my wood retaining wall, I used a 2x4 as a pry bar.