To play as Tails, from the main menu select “Multiplayer”. Then either select “Local Co-Op Mode” or “Online Co-Op Mode”.
If Local, then plug in a second controller and press start (You can sign in the second controller as a Guest if you want). On the level select menu choose a Zone and an Act.
Once confirmed you will be asked which players want to be who. Pick Player 1 as Tails by using and . Confirm once again and the level will start. Beat your desired level and then repeat the process until the achievement unlocks. If choosing online get a partner unless you want to fight to be Tails. Regardless, if your partner decides to stick around you will both alternate being Sonic/Tails every other Act.
Note: It seems people are having trouble unlocking this while doing Online Co-Op. Until it is looked into more I suggest Local Co-Op for this achievement.