There are four summits to Babcock Peak, this traverse climbs all of them from east to west. Begin on the easy slopes to the east of summit #1 (the eastern summit). From high in Tomahawk Basin, the approach is obvious. Follow 3rd class terrain up to summit of #1. Descend to the saddle between #1 and #2. The semi-technical summit of peak # 2 is reached with some moderate climbing where a rope may be helpful. There was webbing here last visit for a rap. Continue around the south side of the ridge up to the summit of #3. Traverse over to #4.
Extra credit (and extra fun): keep traversing the ridge out to Spiller Peak, or over to Moss Peak, or both.
On the central-west side of the La Plata mountains, one finds Tomahawk Basin. There is a fairly decent 4WD road leading up into the basin from the main 2WD road. Drive this to the end, and then hike into the upper basin.