Start at East Rosebud Trailhead, hike toward Cooke City on what has been called the "beaten path". Continue past Rainbow Lake, camp there. Pick a route uphill at 2nd creek descending from above on the right hand side. This puts you on the main plateau at about 11,400 ft elevation. Hike to NW summiting Mt Pleasant along the way. From the summit of Mt Peal have great view of Granite Peak, Tempest, Mt Wood and to the south the Castle Peaks group. Mostly easy hike really. Just need endurance.
Not sure if you could cross the canyon from Peal to Tempest. Maybe there is a route, though I did not try it.
Climbed the Peal Glacier (East slopes) from Phantom Lake
Reached the summit at noon, stayed for a half hour then tagged Mt. Pleasant before a 1pm thunderstorm chased me down. Take the first switchback off the Phantom Creek trail. The map I had showed it branching off the second switchback and it was wrong. Actually, if I were to do it again, I'd come from West Rosebud, over FTD and down the gully that leads to the northern most tip of Froze-to-Death lake. Unlike the slopes further west, it's not too steep and is mostly vegetation, rather than boulders or scree.
This route got the job done, but I can't recommend it to anyone looking for an enjoyable hike. We found a steep but 2nd class weakness (grass and stable talus) in the cliffs below FTD Plateau that allowed us to drop 1300 feet down to just above Turgulse Lake. From about 10,400 ft we embarked on an awful talus hopping traverse to the base of a nasty northwest facing gully leading to Peal's northeast ridge. The gully was full of unstable talus and care had to be taken. From the top of the gully it was an easy talus hop to the summit. Had to regain 1300 ft to get back to camp. Investigated the ridge between Tempest & Peal from both sides and filed it under the "may be possible but not worth the risk" category. Two large notches complicate the otherwise easy ridge. The climbing looked to be at least 4th class, probably 5th, and there was loose junk everywhere.
Climbed Peal from FTD plateau and it was a heinous, never ending boulder hop. Dropped off the plateau down steep slopes to just west of Lake Turgulse and contoured across the basin at ~10400' on huge boulders, some the size of cars. Ascended a nasty n.w. facing gully filled with dangerous talus. Knocked off a huge block near the top that exploded. The n.e. ridge is still a boulder hop, but pretty easy. The south side of the mountain is much more aesthetic with impressive cliffs. Also, we scoped out the connecting ridge to Tempest and it looked very questionable if there is a safe passage. Wish we would have had crampons for Peal Glacier.
Climbed the sE ridge, probably should have a partner and rope. Very airy traverse in the notch and climbing the summit ridge.