Although this achievement unlocks after finishing the final mission, it's really for completing all story missions in the game.
IGN have done a thorough job of creating a step by step walkthru for every mission. I'm currently using this to remind me what's coming next for my Liberty City Minute achievement and its very detailed.
http://guides.ign.com/guides/827005/page_5.htmlIf I were to add one extra tip, I would say never start a new mission without full health and fresh bulletproof armour (bought from any gun shop around the city).