In my setting there is a tidal island fortress similar to Mont-Saint-Michel that is the refuge of important nobility and is therefore a target for an invading army. The fortress also has a library containing an extremely valuable manuscript that the invading king absolutely must have. So there is motivation for besieging such a place.
The tide is strong and makes the fortress an island during high-tide and leaves behind a treacherous mudflat at low tide that is very difficult for men to walk on and is impossible for any cart or horse to cross. The water is too shallow for large ships, but shallow draft boats and rafts can cross.
A talus wall and glacis encircle the island and provide resistance to cannon fire. There is a secondary wall further up the island and a castle keep.
The Island has freshwater wells and several large gardens along with significant food storage space. The defenders have a well trained garrison of 200 men equipped with crossbows, polearms, swords, matchlocks, cannons and even a primitive volley gun
The attackers are several thousand strong and at a 14th century European level, and can do any tactic that you believe would work. No magic allowed
So how could an army with 14th century technology capture a well defended tidal island?