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The Sapphire Key is in a standard chest at Frozen Hall (5-1) The Ruby Key is in the Sapphire Chest at Steel Island (8-1) The Emerald Key is the Sapphire chest at Upper Level (1-1) The Amethyst Key is somewhere in the first 8 rows and does not require the Emerald Key.
Either the Black or White Key is obtained by doing some quest after #19. The other is presumably obtained either in another quest or by unlocking a Black or White chest.
Should you read this message and find it helpful, please consider acquiring the missing information and posting a complete list on the Codes section as a list of Unlockables.