Usually in reference to a girl at a bar he hopes to talk to and show off his expensive bad tattoo he saw in a book -- and then copulate with.
Josh and Trevor move in close and notice three girls at the edge of the bar. Without saying anything, they look at each other with semi-homoerotic undertones and connect with a conquest pound.
A 1st Conquest is the first woman that becomes one of the X's in one's Black Book. the first woman you been going after until you eventually get that ass. It can only be considered a 1st CONQUEST if you come out with her for the first time and have pictures and/or videos of you in action (her face required).