Here is the full list of all 12 Nidhogg trophies - there are 7 bronze, 4 silver and 1 gold.
Get eaten by the nidhogg after nearly allowing your opponent to do the same
Trap your opponent on your sword for a long time
Beat the singleplayer game
Win the faceoff and never lose the arrow in a singleplayer match
100 total kills in one match
Run across your final screen in the castle with your sword cocked the whole time
Finish an 8 player tournament
Let the timer run out in your opponent's last screen and win in sudden death
Win 100 games through matchmaking
Play a match lasting longer than 20 minutes
Intelligence gathered
Dominate every level in one singleplayer game