Here is the full list of all 9 Nutjitsu trophies - there are 5 bronze, 2 silver and 2 gold.
Complete 50 ninja missions.
Finish any game on the Redclaw's Castle, Teikoku no Yousai, and Base Camp Shichi levels.
Finish any game on the Grey Shrine, Yugure Cemetery, and Ushinatta Marsh levels.
Finish any game on the Shizuka Woods, Dangai Heights, and Bamboo Glade levels.
Achieve maximum rank.
Lose 20 foxes that are on your trail by using Smoke Bombs or Shadow Clones.
Hit 30 foxes with the effects of Freeze Bombs or Fire Shields.
Outrun 12 foxes that are on your trail.
Collect 10 acorns.