Drive along Highway 120 until reaching the Cathedral Lakes/John Muir Trail trailhead. Proceed up the trail for two miles until reaching a broad, fairly flat forested area. Leave the trail and hike south-southeast towards Cathedral Peak.
Hike up class 1-2 grassy slopes and slabs and through krummholz whitebark pine stands. If you begin on or wander to class 4 slabs, you have gone too far south (i.e., you have gone too far towards the base of Eichorn Pinnacle). You can avoid most of the whitebark pines by walking through a cleared burn area to the left. When you are level with the saddle between Eichorn Pinnacle and Cathedral Peak, traverse across the peak, crossing some slabs, toward the saddle. Scramble up class 3 ledges, remaining parallel but below the ridge. Eventually, by following this route, you will have zig-zagged back across the peak to just below the summit block. Climb onto one more ledge and into a short chute adjacent to the south side of the summit block. The top of the chute is a good spot for belaying. The final move involves a short traverse on the east side just below the summit block, then a final class 4 scramble up the 15-foot summit block.
A rope and some chocks and slings for the class 4 section.
John Muir first climbed this peak in 1869 via this route.