Double Ring Mail is crafted with Blacksmithing in Mabinogi (armor). This page lists everything needed to make it, checked against the game as it exists today. The interactive planner lives in the Blacksmith Companion.
How to get the manual
The manual is rank 9 and survives 30 uses; every crafting attempt spends one use.
Goblin Bandit: field boss goblin pack found near Dunbarton.
Materials
Expect about 7 attempts per finished item (15% average progress per attempt). Per-attempt materials are consumed on every attempt; finishing materials once per item.
Each attempt uses
5× Iron Ingot — refine from Iron Ore (common low-rank Refining output)
3× Fine Leather Strap — weaving rank 6 on a spinning wheel
Finishing (once per item)
1× Common Silk — buy from Seal Merchant (Mondays) for seals, or weave rank F
1× Siren's Cat Mask — Siren monster drop in Rundal Dungeon