Bogachiel Peak is located along the High Divide trail near Seven Lakes Basin. From the High Divide trail, the peak is a 0.3-mile side trip; on maps it looks like there are two ways to access the peak, but the far better trail to the peak is on the east slope of the mountain.
If you're approaching from Lunch Lake or the Hoh Lake trail, continue east around the south flank of Bogachiel Peak to where a trail junction switchbacks west. If you're coming from Heart Lake, simply look for a boot path branching off to the right. Take this short but steep trail to the forested summit of Bogachiel Peak. While a high point with some very good views, the views are actually better back down on the High Divide Trail.
Camping is not allowed at this summit, and visitors must have a permit to camp in the Seven Lakes Basin area, including Lunch Lake and Hoh Lake.