You do not need to complete everything else. This just means get an A Rank on all the Hero, Dark, and Cannon's Core missions. You'll unlock this pretty fast if your after the all A Ranks. I think either Dry Lagoon or Wild Canyon would be the easiest to complete this, since there requirements are pretty low and can be done very fast. Simply get all A Ranks in one character's stage. Also adding on a lot of lives might be good too. If your having trouble, try to replay some levels and get all the upgrades (such as the air necklace). Does not require you to complete every mission for Cannon's, just the main story. Will unlock once beating the LAST Side of the game. This shouldn't be to hard, and even new players to this game can complete this with a few hours! Does not require you to complete every mission for Dark, just the main story. Will unlock once beating the DARK Side of the game. Does not require you to complete every mission for Hero, just the main story. Will unlock once beating the HERO Side of the game. You receive this by completing the first level of either HERO or DARK story.
You are practically guaranteed this achievement just by turning the game on.