To unlock Buddy Pine and Syndrome you need to play the game until at least Story Mission 8 (Buddy unlocks after you complete Story Mission 7) and you will also need to complete all the Crime Waves (Syndrome unlocks after you defeat him in the final Crime Wave).
Once you have both characters unlocked just go into character selector by holding Triangle. Select either Buddy Pine or Syndrome. Tap triangle to switch to the other character and repeat while selecting the remaining character.
Once they are both in your party the trophy will pop. This can be done in Free Roam on the open world.