Quest #067 Nab the Knife-Nicker - Swinedimples Academy
Quest Requirements: Defeat Shivery Shrubbery with Toxic Dagger while it's asleep until it drops a Broken Blade
Quest Pre-Requirements: 30 Skill Points into the Knife Skill Tree
Reward: Icicle Dirk
This quest begins by speaking to Madame Couteau on the 1F of the Swinedimples Dormitory (in the eastern portion of Swinedimples Academy). In order to accept this quest you will need to have put at least 30 Skill Points into the Knife Skill Tree.
For this quest what you need is at least one person in your party that is capable of putting the enemy asleep and someone equipped with a Knife who is able to use the Toxic Dagger ability. Around Swinedimples Academy you'll find Shivery Shrubbery enemies which are the enemies that you need to defeat for this quest (shown in the screen shot below).
Basically what you'll want to do is put them asleep using Snooze or whatever ability it is you have that puts them to sleep then take them out using Toxic Dagger. You don't have to let the poison kill them or anything like that. If you can't one shot the enemy I would recommend using Oomph on the character before attacking so you don't have to keep putting the enemy to sleep.
I got the broken blade for this quest on the first try but I am assuming I got insanely lucky.