Here is the full list of all 12 Nidhogg trophies - there are 7 bronze, 4 silver and 1 gold.
Beat the singleplayer game
Win the faceoff and never lose the arrow in a singleplayer match
Trap your opponent on your sword for a long time
Get eaten by the nidhogg after nearly allowing your opponent to do the same
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