There are really only 3 modes in this game: Offline Solo, Online Survival, and Online Survival VS. For this trophy only Online Survival counts, even if its online solo invite only and as it states, you have to WIN. If you're in this for a quick trophy, just make an invite only normal difficulty normal length match on your favorite level and make sure to not die.
This gets the job done but will take some time, about 5 hours, and really avoids the fun of the game IE running around like a crazy person with 5 random players killing everything. To each his own I suppose.