She and Powergirl are currently in Kandor. Red Sun enviroment and their powers are waining. So, probably standard needles and ink.
Doesn't make sense, because according to the plot summary, Kara still had all her superpowers.
And I still think her tattoo will last about as long as Superman's 1970s long-sideburns did - which was even less time than his mullet!
DC is still using the solar battery explanation for Kryptonian powers, Post-IC.
Meaning that while Kara still has all of her abilities, those abilites get weaker and weaker in power due to the red sun enviroment and the lack of any yellow solar energy.
With her invunerability not being up to normal levels, she was able to get the tatoo.
Funny thing is, once she leaves Kandor and comes back under the rays of a yellow sun, the tatoo should fade due to her body's natural healing process.
After all, the current Superman has never sported any sort of scars from his many fights. Even the particurally bloody fights he had with Doomsday.