It really depends, first of all you can open only one shell every 20 hours, secondly, after opening the shell you can get one of the three options:
- find a Giant Shimmering Pearl
- find nothing
- squeeze your fingers resulting in a loss of 200 hp (equipment will lower the damage).
All the options have a similar chance so depending on your luck, I'd say no less than 200 days.
P.S. I would also like to add some statistics that I have found just now:
It seems that you have more or less 50/50 chance of getting a pearl. This concluded that, as I've mentioned before, you need around 200 attempts (days more or less)