NS: Triple Jab: One of your most reliable tools, Tomahawk quickly slashes thrice, dealing 2 damage per slash and can combo after anything if done fast enough, the third slash also sends opponents away for you to position yourself better, you'll be using this a lot if you want to deal good damage.
NS Up: Tilt Chop S: One attack not meant to be used everywhere, but useful nonetheless, it deals 5 damage so it's great if you want to deal a lot of damage at once, and it deflects projectiles so it's good to avoid big projectiles coming towards you, but try not to use it a lot since it has a lot of endlag.
NS Down: Tilt Chop L: This attack is great to start combos since it sends enemies up and deals an additional 2 damage at the start of the triple slash, but it only works well if you're already close to your opponents, try to use your other tools to get close and attack.
Slide Attack: A very reliable tool to move fast, it extends your slide through almost the whole screen, and it deals 3 damage, it can also be cancelled to a triple jab for 9 damage in total, the only disadvantage this attack has it that it doesn't protect you while sliding, so if there are any big projectiles or grounded attacks in the screen they might give you trouble.
Charge Attack: Tomahawk Smash: His least reliable move, extremely long startup and end lag, and it is best used in close range since the slash deals 8 damage, you'd get some uses out of this move when trying to corner enemies, but there are other, more effective tools available.
S1:Silver Tomahawk: Great for both vertical and horizontal damage, if you combine it with Feather Toss it's almost certain that you will hit the enemy, aim it to make it harder to dodge.
S2:Feather Toss: Another great tool for ranged combat, each feather only deals 1 damage, but that's not why it's good, since each feather can combo it'll extend your opponent's hitstun, making it easier for you to approach.
S2 Up: Feather Toss: Very niche move, but useful when needed, each feather can absorb one projectile, but it's not very good against grounded enemies, you'll make good use of it when enemies are on walls or above you, so their projectiles don't hit you and you can avoid them.
Extra: Tomahawk man has 20% increased speed when walking, sliding and climbing, making it easier to approach enemies.
Tomahawk has a great mobility, so he's amazing against slow characters, use your melee attacks and quickly get away to win, and due to his good damage output, he's good against weaker characters too.
While Toma is very mobile, he still struggles against characters that can outrun or outdamage him, try to use your ranged attacks and approach carefully