These are necklaces that have similar mechanics to the Charms from Hell Pit.
They are dropped by the 20 Stomachs that can be found in Cafe Au Lait in a hole on Troll Island
Note that this creature has something like a 800k max hit and even with 20 attacks, you'll probably only want to attempt him while wearing earth resistance rings to bring that down a bit. He's got a fairly decent health pool too so expect to go more than a few rounds
The random portions of these drops are a bit different than the charms though.
There are 4 random components to each drop.
<a> <b> Badge of <c> <d>
a:
The creature type that this necklace may offer increased damage to. i.e. Mythic, sea creature, other, shapeless, etc
b:
The amount of increased damage you'll do to <a>
Current options are:
Observer - 0%
Finder - 10%
Challenger - 20% (20 Stomaches Veteran)
Attacker - 30% (30 Stomachs only)
Destroyer - 40% (Gods only?)
Inquisitor - 50% (Gods Only?)
c:
The amount of the stat <d> the necklace provides
Lesser - 1k
Increased - 2k
More - 3k
Much More - 4k
Greater - 5k
Massive - 6k
Impressive - 7k (20 Stomaches Veteran)
Overwhelming - 8k (30 Stomachs only)
Extra - 9k (40 Stomachs?)
d:
The stat that will be increased by <c>
Might - Str
Delicacy - Dex
Sturdiness - Con
Exoticness - Wis
Puzzles - Int
Ornateness - Chr
Increase to damage research:
Order of damage increase. Impressive Delicate, Massive Delicate/Impressive Might/Sturdiness, Greater Delicate, Massive Might/Sturdiness, Greater Might/Sturdiness, MuchMore Delicate, MuchMore Might/Sturdiness