Kuna Peak (3979m) is the third highest mountain in Yosemite after Mt Lyell and
Mt Dana. It is by far the least visited of the three. Kuna Peak is located at the border with the Ansel Adams Wilderness.
The hike starts at the Mono Pass trailhead off Tioga Road (Highway 120) just west of Tioga Pass. Usually two ways to the top are described: via Helen Lake and via Parker Pass. Be aware that there is no way to reach the real summit via Helen Lake. Kuna Peak has two horns, the southern and northern horns. The real summit is the southern one and nothing connects the two horns (there is a deep chasm between the two).
The Parker Pass route is relatively simple. Follow the Mono Pass trail and just before Mono Pass turn left into the Parker Pass trail. The trail to Parker Pass is a straight line that hardly gains any elevation. After Parker Pass the trail is another straight line that hardly loses any elevation. But then (after great views of the valley to the east) the trail bends right and starts ascending via steep switchbacks (with increasingly great views of Mono Lakes and the lakes south of it). The switchbacks take you to Koip Pass. On the other side you can see the Alger Lakes, that the trail will soon coast. But instead you leave the trail at Koip Pass and head up the slope to your right, which is Koip Peak. This is a straightforward class-2 climb. Once at the top, admire the 360-degree view from the Ansel Adams Wilderness to Mt Ritter and to Mt Lyell. The mountain to the east is Kuna Peak. Descend to the saddle between the two and climb the slope of Kuna Peak. En route you will notice the relics of a plane crash. Kuna Peak has several subpeaks but it is not difficult to guess which one is the highest. Just like Mt Dana, it does not have a summit register nor a USGS marker. If you want to bypass Koip Peak, you can leave the trail after Parker Pass and head for the canyon that dead ends in the Kuna glacier. Stay high to the left of the glacier to avoid the ice. The Koip-Kuna saddle is just above the glacier. See my pictures in reverse (i came down that way).
The Helen Lake route is more complicated.
After about 3 kms the southbound Mono Pass trail shrinks and forks: turn right
towards Spillway Lake. The trail takes you to the left side of the lake.
Continue on that side following the creek. The creek first bends left (east)
and then right (south). This will take you to the left (eastern) side of
Climb the ridge to your left any way you want: right away, or on any of the chutes further up. Once on the ridge proceed south. It is a frustrating experience because, no matter where you reach the ridge, there are a number of false peaks, one after the other. The last one is not obvious until you climb it. At that point you see the southern horn. You can continue in that direction but you will reach a dead end, an impassable class 5 wall. Unless you really like those two lakes, there is really no reason to take this route. However, there might be another attraction here. The prominent unnamed peak straight south of Helen Lake (i named it Mt Joyce) offers great views of the Ansel Adam Wilderness, of the John Muir Trail and of the Mt Lyell glacier. You can even descend to the John Muir trail and return from Tuolumne Meadows to the Mono Pass trailhead (but this is a long detour).
Whichever route you take, it shouldn't be more than 5 hours from the trailhead to the northern or southern horn.