Hmmm... I looked in the usual folders below that run launch items, and nothing is there for Fantastical.
Code:
~/Library/LaunchAgents (~ is your users folder)
/Library/LaunchAgents
/Library/LaunchDaemons
/Library/StartupItems
/System/Library/Extensions/
On the Fantastical site they talk about some settings in ~/Library/Containers. In there a Fantastical 2 launcher folder. I'm wondering if removing that would do it? Make sure you have a backup first of course.