Quick Reference Guide to Catch Balack the Banished
Goal 1) Gain entrance to Balack's Cove
Buy the Ancient Lantern at Cape Claw. Loot Dragon's Ember at Dracano. Craft Balack's Lantern and Balack's Cove opens for you.
Goal 2) Growing your Stilton baits
Loot Vanilla Beans at the Jungle of Dread from the Pygmy Swarm Mice. Craft some Vanilla Stilton Cheese and head to the Cove. Catch the Lichs for their loot. (Acronym trap recommended)
That allows you to craft the Vengeful Vanilla Stilton cheese.
You'd now be able to catch Balack the Banished Mouse. (Ancient Box Trap recommended, Acro/Ice Maiden works too)
Repeat Goal 2 as necessary.
Following each link above will yield a more in-depth walkthrough.
(And I'll fit in all the images later)
(and many thanks to the MouseHunt Kitchen, for most of the info)