From the Main Menu select Missions; now choose your character, what type of mission you want to do and the specific mission you want to complete. Successfully complete all of the missions to earn this trophy. There are 7 characters to choose from; Raiden, Raiden Ninja, Raiden X, Snake, Pliskin, Snake (Tuxedo) and Snake (MGS1). Each character has their own missions, some more difficult than others; Snake (MGS1) has by far the most difficult missions. This trophy will probably take a few sessions to complete, be sure to save your data before quitting the game or turning your console off. There is no auto-save function and if you don't save you'll lose any progress you've made.
Raiden / Ninja / Snake / Pliskin / Tuxedo Mission Guide.
Snake (MGS1) Mission Guide.