It upgrades like any other gun until you get to the last upgrade orb.
Then you need the Crux of Crota exotic orb which only has a chance to drop from the hard raid.
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I have no intention of upgrading this to Necrochasm (although I have 2 more Husk of the Pit I could evolve to Eidolons). As horrible as this gun is in PvE it holds its own in the Crucible (maxed stability, close to medium range). This way I can use an exotic Special (Invective) or Heavy (Gjallarhorn, Thunderlord while doing the Super Good Advice bounty) and level those. I guess there's something unnerving about having a max Rate of Fire weapon fired at you :-p.