Here is the full list of all 13 Nidhogg 2 achievements.
Win the faceoff and never lose the arrow in a singleplayer match
Beat the singleplayer game
Kill yourself with your own arrow
Get eaten by the nidhogg after nearly allowing your opponent to do the same
100 total kills in one match
Dominate every level in one singleplayer game
Let the timer run out in your opponent's last screen and win in sudden death
Play a match lasting longer than 20 minutes
Beat the singleplayer in under 20 minutes
play a match with old school settings
Trap your opponent on your sword for a long time while moving it up and down
Finish an 8 player tournament
Win 100 ranked games through matchmaking