How to Unlock Durahan Guide
In order to unlock the Durahan Monster you'll first need to raise a Monster to a high enough rank that you're invited on an expedition to the Parepare Jungle. Here you'll find an Old Sheath hidden away in a mausoleum in the central portion of the adventure behind a large pumpkin obstacle.
Important off topic note, the mausoleum this is found in is right next to Tusk Tower which has the Gold Peach; an item that drastically increases your Monster's lifespan. This is the rarest and most valued item in the entire game which is why I am making a point of pointing it out now.
Back on topic, you might not get the Old Sheath your first time cleaning out the mausoleum but keep returning here until you do - this is the only building that has it throughout the entire area. Once you have this Old Sheath you'll want to hold onto it for a bit, at least long enough for Auntie who runs the item shop to mention a set of stolen swords.
It might not happen on your first visit, just keep the Old Sheath in your inventory and keep returning to Auntie's store on days when she isn't holding a sale. Eventually the dialogue will happen and it'll advance the quest forward.
Assuming that you have a Monster that's A class or better, on the first week of February you'll be invited to the Double Edged Tournament which takes place at the end of February. The prize for winning this tournament is an item called the Double-Edged Sword.
When you use the Double-Edged Sword as a secret seasoning during Monster combination you'll get the Durahan Monster. That's all there is to it!