This is a fully local multiplayer game and you need to know the start button of the second player which is V from your keyboard and the only one needed to enter the room and confirm the ready state. All achievements can be unlocked by actively using just the first player after the match starts.
Go to blue map levels and select Moat. Crouch in water until you die.
One With Water
Also on the Moat map. Kill yourself there sometimes by crouching in water.
You display an affinity for offing yourself
If you jump and slice just as you’re about head level with an opponent, you decapitate the enemy.
You need 10 heads for two achievements.
The heads of five samurai hang at your belt
Ten Head Belt
Go to where an enemy is and use your sword down to kill without moving.
You dispose your foes without moving
Go to red map levels and select Tops. Destroy all the bamboo above the spikes. Bamboos will grow after a short time so you need to cut them all down with reasonable speed.
Trying to break the game by destroying all the bamboo