Under the challenge menu, there are two forms of challenges - online and local. You must select the online challenges to unlock all the "multiplayer" trophies. If you already know you have a friend with a PSN who has played the game, skip the next paragraph and follow below.
If you do not have a friend who played the game, you can still solo this trophy. Create a second PSN account (unless you have one), which connects to the PSN network. Once you have a second PSN account, ensure you are friends with your main account. Play the game under your second account, and complete any of the online challenges. I recommend Hard Challenge 4, as all you have to do is run, and it will net you the following trophy:
Once you beat the challenge on your second account, you can log into your main account and complete the same challenge as you did on your second account, or the challenge your friend has completed. Go to the Online Leaderboards, and press triangle. This will display your score, along with your friend's, or second account's. You do not need to beat the other score.NOTE: Your score will not post to the leaderboards immediately. Mine only took about 5 minutes, but I have seen from others it can take days.