This can only be unlocked as the original Wolverine, not the (Cowl) variant, Wolverine is unlocked by completing level 4 'Rock Up At The Lock Up'
Once you have a wolverine character either in the level or freeroam (head into the Control Room of the S.H.I.E.L.D Helicarrier and open the mission hub (Area in the middle) and choose any level to play in freeroam and choose your Wolverine character.)
Now simply have all of your hearts removed by enemies (Or a second controller) and Wolverine will turn into a skeleton and he will now regenerate slowly.
Once all his hearts are back your achievement will pop. (May pop once his body has regenerated too)
Here's a video