Many of the games arenas have stage transitions that result in combos of 10 hits or more, allowing you to earn a 10 hit combo through just a single input.
Go to practice mode, choose a character and the Wayne's Manor stage. Push your opponent all the way to the right, and press + to do the level transition. Wait for the animation to end, and you'll see you've landed a 16 hit combo. This counts as landing a 10 hit combo for that character.
Now go back to character select and repeat these steps for all 24 characters. Work your way through each character in order so you can keep track easily. Once you've done this with every character, the achievement will unlock.