Why did the black ink turn blotchy and look blown out after my first laser treatment? (Photos)

Thanks for posting your picture. Tattoo removal takes multiple treatments. 
Your tattoo looks reasonable in terms of one treatment. I would not expect a uniform fading of ink. It really is patchy which is normal 
Best wishes 

That is exactly what your tattoo should look like after your 1st laser tattoo removal session.  Laser tattoo removal works by breaking up the ink into much smaller molecules that your body can absorb.  The area's that appear "blotchy" are the area's the laser has destroyed the ink to a sufficient size that your body was able to reabsorb.  Your size tattoo will take up to 12 sessions to complete and it will fad less and less with each treatment due to the remaining ink being so small the laser has a harder time vaporizing it so don't give up.