These trophies are fairly self-explanitory, simply play through both the Mortal Kombat and DC story modes until you have completed the game and unlocked Shao Kahn and Darkseid.
While I realize that information wasn't solution worthy, this little bit is. While playing this game, I noticed that if you accidentally were playing as "Player 2" for some reason the trophies wouldn't pop. I had a wired controller in and hadn't noticed the wireless controller had been P2. The standard progression trophies unlocked, however at the end I didn't unlock the characters nor did I earn these trophies.
Fear not, you don't need to replay the story mode if this happens. Simply change the controllers and the trophy should pop after clicking each story and watching the endings, the characters will unlock as well.