This trophy gave me some problems, so here's what I did to get it to unlock:
I loaded up my existing single player game and turned on multiplayer from the menu. I then launched into space and summoned the Space Anomaly. Go up to the left and find the station terminus. From there, you should be able to see other players' bases that are available to warp to.
Choose a base from the normal list of players ( not the community spotlight) and download the base. It took me a few tries to find a base that would download successfully, but once you do warp to that base. From other guides, it seemed like some people were able to just interact with the base computer at this point to get the trophy, but that didn't work for me.
If you have the same problem, go to your ship and make a manual save. At this point, I went into the menu again and turned multiplayer off and then loaded the manual save I just made. Once the base loads, just go and interact with the base computer and the trophy should pop.