Piece 1: the stealth hat. (Shadow Queen's Cowl) (See witnesses and guards through walls. Apply distracted upon successful pickpocket.)
Piece 2: pickpocket booster
Piece 3: +5 seconds to lockpicking, better chance to force locks
Piece 4: Reduce area of detection of where you can be detected while lockpicking
Piece 5: Cheaper Stealth
Piece 6: Better Stealth
Piece 7: Reduce detectability of assassinations
Piece 8: Reduced bounty gained from thievery and trespassing
Piece 9: Reduced bounty gained from assaults and murders
Piece 10: If you assaulted someone and kill them, and have no other witnesses, that bounty and heat is cleansed. Aka: Kill the witnesses, the bounty is cleansed.
Piece 11: Sithis Set from Hews Bane
Piece 12: Increase the duration of the stun from sneak.

Order of gain can be differentiated, or the items are related to specific pieces like the Shadow Queens Cowl.
These Items would individually have stealth-benefitting perks, but can be worn together. With the full set one basically becomes the master of shadows and stealth.
Some pieces would be a bit more difficult to obtain than weapon sets, as the lead has only a chance to drop, whereas some weapon sets are guaranteed to drop on completion.

For those who say Mythics are easier to get than Weapon Sets: They aren't. I did 5 bouts of Asylum Sanctorum in 30 minutes. It's easy to do. Perfecteds however, Veteran version may be a challenge.
Likewise, if there are Perfected versions of this set, all pieces leads should drop from Veteran stuff. As with the normal chance system, that means they'll be much more a pain to get than perfected weapon sets.

Perfected Stealth Based Mythics:
Perfected Shadow Queen's Cowl: Max Stamina / Reduced Sneak Cost / Reduced Sneak Penalty / Increased Sneak Speed / Reduced detectability radius while sneaking / etc.
Other Pieces, other possibilities.