The Mythic stones can be found on any floor below 60. They will randomly appear after having all of your cursed tools blessed. They will not appear until your cursed tools have been blessed.
Alternatively, Mythic stones can be obtained by winning the rock paper scissors game 40-49 times in the Town Cottage.
If you manage to find a Mythic stone, you can bring it to Saibara and he will upgrade your tools to the final level. Your blessed tools can be upgraded to Mythic Tools, which is the 7th and final level of a tool. It will cost you 50,000G and 2-3 days duration for each tool you wish to upgrade.