Catchable Epic/Rare monster Caves
Miracle Sea expert 8- Tresha (common)
Roll 4, 2, 1, 3
Epics:
Volcano expert 10- Meniss / Danshee (Mutant)
Roll 4, 5, 2
Stone Vault expert 6- Seafoam
Roll 2, 3, 3, 4, 1
Canyon expert 13- Cygness / Cranie (Mutant)
Roll 5, 1, 2, 2, 3
Sealed Space expert 8- Pattapilla / Pattairy (Mutant)
Roll 1, 3, 1
Sealed Space expert 15- Neo / Neor
Roll 1, 3, 2
Thorny Forest expert 10- Pinster / Scister
Ocean Abyss expert 6- Whalorn
Rares:
Jungle Veteran 5- Octobud
Miracle Sea Veteran 10- Crabby
Volcano Veteran 10- Branchy
Stone Vault Veteran 10- Ricky
Canyon Veteran 15- Chimp
Sealed Space Veteran 15- Lupa
Frozen Cavern Veteran 15- Freezy
Chaotic Swamp Veteran 15- Stinger
If you find more please feel free to post.
The epics will have a 1%-2% catch rate so you will have to use quite a few cards to catch them.
Edit: Removed the part about the 100% on first catch. It does not work anymore.