You will fight Galactus at the end of the Skrull Cityscape level towards the end of the game. You'll unlock this achievement by beating him and his corresponding level.
In order to beat him, you must first activate three consoles that weaken his power. After you have activated all three, you will take control of Silver Surfer who is flying around Galactus. You'll have to press the button corresponding to the on screen quick time prompt. Once he is hurt, a third of his health bar will drop and you will have to repeat the steps two more times (for a total of three) in order to finally beat him.
For extra, visual help, follow the video guide below. This guide is a walkthrough of the whole level leading up to Galactus, if you want to skip directly to the boss fight, then go to the 22:30 mark.