Its in-game description reads "Sword with the power of an Atlamillia."
The Atlamillia Sword is one of Monica's ultimate swords. Its stats are very high, but unfortunately it only has a 4-hit combo. Its elemental stats aren't very balanced, either, but this sword is very effective against plants or chill-based enemies because of its high Flame stat. It's a good sword to possess, but the Island King is far better as a 4-hit combo sword.
Most of the time, you'll obtain this sword with the build up system. It cannot be bought or invented.
The Atlamillia Sword is a high-tier weapon (Tier 8), meaning it'll gain 6 Synthesis Points (SP) per level-up.