I cleared a long bank of brush (honeysuckle, Japanese Heaven, multiflora rose) many years ago that totaled about 1/2 acre. Working on a 30 degree bank made it more difficult, but was still doable with a chainsaw, axe, lopers, long handle hedge trimmer, and assorted other tools. Once it was hacked up I just kept it mowed with a walk behind and in a few years the invasives died off.
Were I to do it again (not on a bank) I would selectively chainsaw the large diameter stuff, drag it out, then get a brush hog or flail mower in there to mow it off. If you're talking 5-6' high and dense jungle, I would hire it out to a forestry mulcher.