Climb the drainpipe up the side of the LA Public Library (just like in the Quarter Moon Murders case). Climb up the scaffolding to get onto the main roof. Walk straight ahead to the other side of the roof. There are two large tanks on that side. Climb up the wall in between the tanks, and the badge is on the roof in the middle of this area.
Find all the badges with this post on the L.A. Noire Badge Pursuit Challenge.
