Kinak spoke in depth about avatar unlock conditions in recent podcast 52; Avatar 31 in particular: "hahahahahahaha, you totally can get that. That is not an easy one. For what it's worth, that's one of the PvP avatars, that requires not just wearing a specific outfit, but doing something specific." (paraphrased). Presumably not from something explicitly unearthly then. From the updates in that time frame, the bolded ones below seem most likely (purged the likely non-relevant updates):
October 8th, 2013 - Automatic weapons are now a little more… automatic.
October 18th, 2013 - Zack is ringing in the new season with a new mask. [abstract domino mask; 1 coin]
November 30th, 2013 - Zack hopes you like puzzles, because he's got a doozy. [black tablet shard; 2 coins]
December 14th, 2013 - Added some new knife-related content.
January 6th, 2014 - Zack has acquired an appropriately chilly new unearthly item. [blade of the snows; 1 coin]
February 15th, 2014 - Hid a few more masks in the museum.
March 26th, 2014 - Campus just got a little more metal.
March 28th, 2014 - Zack's added his two coins to the metal revival. [Stainless Skulls helmet; 2 coins]
April 4th, 2014 - The Garottes aren't a metal band, but they're still getting an update.
April 9th, 2014 - Spears have joined the ranks of updated weapons.
April 24th, 2014 - Made some updates to long-ranged combat and related items.
April 25th, 2014 - Put some literal spring in your step with Zack's new offering. [Reflexcoil pants; 1 coin]
June 5th, 2014 - Zack is offering a mysterious chain to begin his fourth round of the seasons. [charmed chain; 2 coins]
32 is also available somewhere in this timeframe; maybe likely unearthly.