A long time
I would use a Revlite SI. Because of the size and darkness of the tattoo, you can expect 15 + treatments. The Picosure is also an option, it would be a bit faster but twice the price probably.
Laser Tattoo Recommendation
I would recommend the new Picosure nanosecond pulsed laser from Cynosure. It looks as if there is some red pigment also which would respond best to the Medlite C-6 Q switched laser also from Cynosure. You can go to cynosure.com for more information. We have both lasers in our clinic. I'm not sure what state you are in, but check for a clinic that can offer both of these lasers. Remember that many treatments spaced 6-8 weeks apart are required to fade a tattoo, so it is a committment in time as well as money. The treatments can be quite uncomfortable, although use of the Zimmer cool air during treatment and ice packs before and after are helpful. I recommend having your treatments done in a medical office so that you can be given prescriptions if needed for itching (which sometimes happens as the ink is broken up).