Mount Beelzebub is one of 21 7,000footers in Chugach State Park. It is a tough summit to reach because of a lengthy approach and very rotten rock. FA: Art Davidson, David Meyers, Nick Parker, and Mike Judd, August 1965
There are 2 paths into the wrath of Mount Beelzebub. 1) Start hiking from the Eagle River Nature Center along the Historic Iditarod Trail. Hike 10ish miles passing the South Face of Mount Yukla. Once you reach a stream (a creek that flows from the west side of the Twin Falls drainage), go up a hundred feet or so and look for a small climber's/hunter's path that goes steeply up to the right. Follow this trail up 3000 feet to a valley. Then, keep heading up to a 5000ft+ pass followed by a descent to Blue Eyed Lake. This is where you can access the West Ridge of Beelzebub. If you want to climb the North Ridge, continue up through Inferno Pass and onto the West Branch Eklutna Glacier. Make a long arc around the North Ridge.
2) Hike, bike, or 4-wheel in along the 12+mile Eklutna Lakeside Trail. Once at the Serenity Falls Hut, find a small trail on the east side and follow this up the east side of the Eklutna River up and over some falls to the snout of the Eklutna Glacier. Ascend the snout via ice/snow ramps and head up the Eklutna Glacier taking its West Branch to reach Beelzebub's base. Note that nowadays it requires some AI 2 climbing to get onto the Eklutna Glacier.
-Four wheelers are only allowed on the Eklutna Lakeside Trail Sunday-Tuesday. -At either trailhead, you will need to pay a parking fee. At Eklutna, it's $5 or a year's Chugach State Park parking pass. At the Eagle River Nature Center it's $5/day or $10 for 3 days.
There's a few campsites along the Eklutna Lakeside trail, but aren't really useful for this trip. Also, the Serenity Falls Hut requires reservation and a fee of $5/night. It is a great jumping off point to get onto the Eklutna Glacier. About 3 miles up the Eklutna Glacier stands Pichler's Perch, an A-frame hut maintained by the Mountaineering Club of Alaska. As such, this hut is for members of the club only. It's super easy to become a part of the club and costs $15/year. There are a few campsites including a few nice spots near the Twin Falls drainage along the Historic Iditarod Trail. Of course, you can camp most any place. Make sure you practice bear safe camping if camping down along the river. Otherwise, there are many a good campsite to be had up the Twin Falls drainage, near Blue Eyed Lake, and on the Eklutna Glacier.
Northeast Ridge Take the glacier between Peril and Beelzebub up to near the top. Look for an obvious scree slope (or snow slope in winter and spring) cutting through rocky cliff faces to access the North Ridge. Follow the north ridge up and around many genarmes. The climbing is mostly exposed 3rd class with a few sections of 4th and easy 5th class climbing. Also, the rock is particularly rotten even for Chugach standards. So, beware!
West Ridge I don't know too much about this route. It appears you'd access this route by climbing gullies up the south side to reach a saddle between Beelzebub and the Devil's Mistress. Then head up the ridge weaving around the many gendarmes to the summit. The route is probably comparable to the North Ridge route.