It is recommended that this route is done in a counterclockwise direction, that is, hiking north and west from the trailhead, then south across the summit, then east back to the trailhead.
From the Horseshoe Meadow trailhead, hike up the Cottonwood Lakes Trail to the New Army Pass Trail. Continue up to the top of New Army Pass.
From the summit, hike south to the saddle between Cirque Peak and Peak 12,525'. From here, there are two options. The shorter, more interesting route traverses the north face of Peak 12,525' over class 2 boulders, then turns south and crosses a large, sandy flat to the saddle east of Peak 12,417' and descends directly to Chicken Spring Lake. The longer, class 1 option descends west down sandy slopes to the Pacific Crest Trail, then follows the trail to Chicken Spring Lake. From the lake, go southeast to Cottonwood Pass, then follow the trail east back to the Horseshoe Meadow trailhead.
From New Army Pass, hike around the High Lake cirque, following the Sierra crest directly to the summit. Though not on a trail, this is easy class 1 walking through sand and boulders.
A good pair of boots.