From the Main Menu select Special then Boss Survival. Boss Survival has 3 difficulties and you can complete it on Easy for this trophy. You will have to fight through all boss encounters (except Fortune) and two enemy encounters with limited gear. You can also select between Snake and Raiden; I recommend selecting Raiden as Snake isn't a "fan of blades" and will end up fighting Solidus with his bare hands. Each encounter (except Vamp) has at least 1 Ration somewhere in the area, be sure to pick them up to give yourself a better chance at survival. This trophy will appear at the score screen once you beat all the bosses.
Olga Gurlukovich > Tanker Hallway Ambush > Fatman > Harrier II > Vamp > Arsenal Tengu Ambush > Metal Gear Rays > Solidus Snake