Joe's Guide to Acadia National Park describes the route:
The Beehive is the majestic peak that overlooks Sand Beach from the northwest. The hike up the Beehive Trail (aka. the Beehive Cliffs Trail) is a thrilling Acadia classic, but it is not recommended for anybody with a fear of heights. This ingenious route heads right up the steep south face of the peak and includes granite steps, iron rungs to climb up, and several handrails for exposed rock scrambling sections. Those who control their fear of heights are rewarded with incredible views of Sand Beach, Great Head, and the surrounding area.
WARNING: This hike is not suitable for small children or anybody who has a fear of heights or who isn't steady on their feet.
For those wishing to challenge the Beehive, there are Strava segments for the ascent only and for the round trip. Start at the Beehive trail/map/interpretive sign about 30 yards up from Park Loop Rd. Run from this sign to the top of Beehive, tap the summit marker, run back down Beehive trail. You have to stay on the marked trail (there are a couple of places where you can FS ~5.6 off-trail that would cut via ferrata course).