This achievement is extremely easy to get (I got it on my first playthrough with Sensei) since the character is uber-broken. Just slash your way through levels. You can also perform a 360 with your stick to execute a powerful all around attack.
Weapon type do only change the alternative attack, and do not alter the way Sensei swings his sword. However, the LEVEL of the weapon increases the range of the energy wave emitted by the sword. Be sure to reach lvl 3 as quickly as possible.
(tip : at the begining of the game, grab the red powerup, then immediatly after the green one. You'll get a second green 20 second later, thus making you lvl 3)
Forget the alternative attacks, though. While the dog is cute, its attacks are garbage.
Don't forget that his katana is able to destroy nearly EVERYTHING, including energy balls and poison clouds. It can also strike through walls.
Edit : the dog rocks. He is here to tag enemies, and does it very well. However, what Sensei throws at them is pathetic. <3 ninja puppy ^^