Arcade Mode is a single player mode where you fight through 6 normal battles and then a final battle with Galactus. You must beat the game with all 36 characters to view thier endings and get this achievement. The MAIN ACTIVE character that is in control when Galactus is defeated will have their ending shown. For instance, if you are in control of She-Hulk but you call Felicia to assist and the assist move finishes off Galactus, then it will be She-Hulk's ending that you will receive.
If you are not very good with one character but need their ending, I'd suggest beating down Galactus with two of your strongest characters and switching to the one you need when his health gets low. If you are fairly good with everyone, I'd suggest you keep picking characters you have not viewed the ending of in your team, then it won't matter who hits Galactus last.
There is also an ending for allowing Galactus to beat you and then letting the continue countdown timer reach 0. You will need this ending as well.
You can see who you have beaten the game with if you enter "Gallery" and then "Character Endings".