As you make your way through the Undead Asylum, you will eventually reach a room where you encounter the Area boss- the Asylum Demon. You are not prepared to engage him at this point so quickly run through the door on the left and make your way through the next hallway, where you will find your character's starting shield and weapon. Progress through a fog door and you will reach an area with a set of stairs leading up. About halfway up the stairs, a giant ball will be released (WATCH OUT!) which will smash a wall at the bottom, allowing you to access a cell where you can interact with a dying Oscar of Astora.
Talk to him, answering yes when asked, and you will be given the Estus Flask and unlock this achievement.