This requires you to complete the story, and then complete some fights a second time.
After you have completed the story, go to Single Player> Story Mode> Chapter Select.
Search through the chapters for the ones that contain two playable characters. You can tell this because underneath the fight it will show which character you have completed it with highlighted in green with a check mark, and a second character will be listed as well, but grayed out. Load up those fights, and complete them as the other character. Some cutscenes and dialogue are different, so that's kind of fun. Once you have completed 70 total fights, you will unlock the last 4, which allow you to play out the alternate ending from what you initially chose. Once you have completed this alternate ending, the achievement will pop.