If you're still missing some achievements after Arcade Mode and have a second controller, second console, or a friend to help you out, it'll be much easier to get the achievements this way instead of hoping to get them by chance. You will have likely picked up a few of these on the way to Stage 8, though.
The first achievement to look out for is to win a round without having the enemy hit you, which obviously will be a lot easier if you're playing against another controller that isn't giving any inputs. If you don't have a second controller, it's easiest to get this achievement against Knuckles in Arcade Mode.
The next achievement is for destroying all of your opponent's barriers in a match, which is done by repeatedly attacking their barrier while they have one up. If you've set the maximum amount of barriers to 1 in Arcade Mode, you most likely already have this achievement, but if you don't for whatever reason, have your second controller or your friend hold down to keep their barrier up while you whack away at it.
When fighting Amy or Bark in Arcade Mode, there's a chance that they'll use a particular attack to squish you, leaving you in a flattened state for a few seconds. If you haven't been fortunate enough to get squashed in their stages, simply set your second controller to either Amy or Bark and have them use their move on the person who wants the achievement. For Amy, her attack is called Magical Hammer, and only requires you to punch while also making a down input (/ + /). Bark's attack is called Crush Punch in the command list, and is performed in the exact same way.
This last achievement is the easiest of all twelve. At any character select screen, press while your cursor is over Amy, and Honey the Cat will appear instead. The reason you shouldn't have done this your first time through Arcade Mode is so that you can fight a doppelgänger, but now that that's out of the way, you can run through the game as Honey without having to worry about it. If you try this on the online or offline multiplayer modes, you can also select Metal Sonic in the same way when your cursor is over Sonic, as well as Eggman when selecting Bean the Dynamite.
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