In our trip, we combined UN13,340 with UN13,222. Therefore the mileage & elevation estimate from 13,222 are based on having first completed 13,340 and then the following route over to 13,222. Most of the account below is from our personal records.
From the saddle east of the true summit of UN13,340, you may wish to tag the 13,315 summit and then proceed along the connecting ridge to 13,222. We did not take that ridge because of threatening weather. So, we decided to lose the elevation and began a plunge-step descent in the scree back down the ascent couloir we had used for 13,340 for about 500 feet until things leveled out a little. Then we contoured for a little while before heading back up to a saddle just south of the 13,222. The task of gaining the next saddle was difficult because it was mostly over slickened, medium -sized boulders for quite a distance. As we approached the saddle, the boulders relented some. We then walked along the ridge north, past one minor point and to the base of the cliffs of the 13,222 summit block. From a vantage point further away, we had spotted what appeared to be a possible route from this side up through the cliffs to a steep slope up above that would lead to the summit. So we explored up a steep, narrow gully that led up for about 50 feet and then ended abruptly. Above the gully, it appeared we could advance a little further, but beyond there, all we could see was a near vertical rock wall that would require technical ascent and gear. Because of the on and off rain and very dark clouds approaching from the south, we knew there would not be enough time to mount a technical ascent, so we decided to retreat back down the gully and contour at the base of the west cliffs across the face of the summit block to the north ridge. (Note: if using Google Earth, it does a very poor job of representing this summit block area.)
This slightly descending contour was across extremely loose and unstable scree. If we had been gaining altitude, it would have been very difficult. Even gradually descending, it was hard enough. After about 15 minutes of struggling across, we turned back up a steep slope of scree, using the aid of a small outcrop of rock for an occasional hand hold to assist and shortly gained the ridge north of the summit block. We proceeded along the ridge toward the summit. In a short distance, we came to the summit block. The route we followed is too complicated to describe, but for the most part, we followed along the ridge, working both sides, and doing a series of 3rd (perhaps 4th class) moves to ascend. The route took us across the head of a precipitous couloir on the northeast side, across ledges and up other short chimneys, etc. for nearly 200 vertical feet. On the wet rock, we had to be extra careful. We were so concentrated on the route, that we never really noticed the exposure. Had it been a nicer day, and had we not been so aware of the oncoming storm and the need to get to the top as rapidly as possible, we might have been more intimidated. But we made the entire ascent without aid or protection. Near the summit, things leveled off and amid rumbles of thunder nearby, we raced to the summit cairn, tagged it, took a quick look around and headed back down. This was no place to be in a thunderstorm, and we wanted to get off the summit block before the rocks became wetter from a serious rain. For another account of this NW ridge, see the link provided to a report by "Furthermore" on ListsofJohn.
As we headed back down, we were able to follow our ascent route closely, even though there was not time on the ascent to make many mental notes as to exactly how we ascended. We did take note of three small cairns on the way up and those three helped to guide us down. Hoping as we descended for the serious rain to hold off for a little longer, we hastily made our way back to the more level ridge and then began a descent on the scree, straight down into the basin west of the summit. Within another 15 minutes, we were out of the scree and onto the tundra. Another 20 minutes got us back to the cabin. From here, you can pick up the trail that accesses Porphyry basin and descend back to the Middle Fork trail and return to the trailhead.
Links to other information, routes & trip reports for this peak that may be helpful.