No idea. While I can't speak for anyone else who has been grinding for it, but mine didn't drop until more than 400 kills. Sad thing is that you can buy it at the very next island in the full release.

It's just luck, I didn't grind and got mine like after 10 minutes inside the tower.
EDIT: And I got another one 6 minutes after posting.

I have heard in other discussion boards (think it was gamefaqs) that the drop rate for the thorn whip in reimagined is around 0,4%. Although I dont know how that compares to other entries of the series.

I got my when fighting the Cactiball. Don't recall having to grind for it, though.

isn't it available in the shops not much further along in the story?

Originally posted by 1stplayerz:

isn't it available in the shops not much further along in the story?

It is the very next island you visit... just past the one you play in the demo.