Here is the full list of all 12 Nidhogg achievements.
Beat the singleplayer game
Get eaten by the nidhogg after nearly allowing your opponent to do the same
Win the faceoff and never lose the arrow in a singleplayer match
Dominate every level in one singleplayer game
100 total kills in one match
play a match lasting longer than 20 minutes
Win 100 games through matchmaking
Finish an 8 player tournament
Let the timer run out in your opponent's last screen and win in sudden death
Trap your opponent on your sword for a long time while moving it up and down
Run across your final screen in the castle with your sword cocked the whole time
Intelligence gathered