I did this on your final Murder mission "The Quarter Moon Murders".
This is a great mission to do this on with the help of Rockstars Social Club site because there are 7 different places where you find a letter, and finding each one of those updates your stats on the social club site. I did this between finding those letters and checking the site and ended up with 55k of damage, so I wasn't wasting unnecessary time getting way more.
50k GS Achievement = '
'Out Of The Blue
' - Portal: Still Alive
100% Retail: Dead Space, Green Latern:RoTM, Clive Barker's Jericho
100% Arcade: Shadow Complex, Harm's Way, Portal:Still alive, Wolfenstein 3d