Falcata is crafted with Blacksmithing in Mabinogi (weapon). 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 2 and survives 30 uses; every crafting attempt spends one use.
Alby Advanced Hardmode: advanced hardmode run of Alby Dungeon (Tir Chonaill). Refined Dustin Silver Knight Helm manual reward. Drop any item on the hardmode altar behind Alby's normal lobby, up to 8 players.
Materials
Expect about 7 attempts per finished item (16% average progress per attempt). Per-attempt materials are consumed on every attempt; finishing materials once per item.
Each attempt uses
10× Iron Ingot — refine from Iron Ore (common low-rank Refining output)
5× Silver Ingot — refine from silver ore. Mine it in Barri Dungeon or north of Tory Ravine
5× Mythril Ingot — refine from mythril ore. Barri Mythril Mine/Advanced, or L-Rod ore deposits