Stutter Dashing: Quickly double-tap a single direction (either left or right) and press the attack button. Do this back and forth across the stage to keep enemies fro attacking you. A bit slower than normally attacking, but very useful to regroup enemies and keep yourself from being damaged. Most useful for harder difficulties.
Shake-off: When an enemy is comboing you, you won't have enough time to run away or attack them, especially if there are multiple enemies grouping on you. Press 'R' to do your instant spinning aerial, which damages you a fixed amount per enemy you hit. It's worth it to do if the recoil will do less damage than the enemy's attack, which is usually the case.
Locking: By positioning your regular attack hitbox (varies between each turtle) at the very edge of an enemy's hurtbox, you can mash the attack button, and your combo will never finish. Keep pressing attack until the enemy you are locking dies.
Combo Interruption: Mashing the attack button will automatically combo, by waiting a certain number of frames between hits, you can never finish your combo and can completely kill an enemy with more health without knocking them down. Very useful if you're hitting multiple enemies on-screen at once
Charged Attack: By holding down the attack button, you charge a bar under your health. The more charged the bar is, the more powerful attack you unleash. You are vulnerable during this time period, however. Each turtle's charged attack is used in each run, but Donatello's is by far the most powerful and versatile.
Juggling: If you're at the edge of a screen, mashing the attack button can sometimes keep enemies in the air, pressed against the screen. You can kill them by 'juggling' them before they hit the ground.
Super Slide: Donatello only. By holding down and attacking, you sweep at the enemy's feet. The second hit knocks the enemy upward a little bit, so if they're at the edge of the screen, you can infinitely super slide and kill them by juggling.
Uppercut Juggling: Mikey only. By holding 'up' and attacking several times, you launch yourself and your enemy into the air. By pressing 'b' in the air several times, you can kill a standard health enemy with one chain.