Azurine Cave can be found on the northwest section of Apophyll Beach. Surf northwest until you reach a small pathway that bends to the right. A huge diving area can be found here. Dive and locate a small diving spot near the center to resurface to an enclosed area leading to the cave entrance.
The Diamond Ring is found on the southwestern house by the diving spot northwest of Apophyll Beach(K-Area). The Diamond Ring can be found on the bottom-left house underwater. Return the ring to the woman in Jasper Ward. This is part of the Klefki Sidequest.
Crying Pokemon in the cupboard
On the underwater K-area by the K 33 House lies a sick and crying pokemon hidden inside a cupboard. Give the poor pokémon an Antidote or a Pecha Berry to receive Mudkip.
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!= has key ; X = no key
West of Azurine Island
Refer to this as the F2-Area.
East of Apophyll Beach
Refer to this as the F-Area.
From Top to bottom; F1(!), F10(!), F14(!),
F19(X), F22(X), F26(X), F34(!).
North of Apophyll Beach
Refer to this as the S-Area.
1st spot: S20(X), S28(X).
2nd spot: S3(X),S4(!), S5(X), S9(!), S12(!).
Northwest of Apophyll Beach
Refer to this as the K-Area.
From Top to bottom; K2(!), K5(!), K8(X), K17(X), K19(X), K22(!), K25(X), K28(X), K33(!).