The Ancient Weapon is a powerful end game weapon for Christina. We first learn the location of where the Ancient Weapon is early on in the game, but cannot come back for it until MUCH later.
While at the Love Engine in the Sweet Tower, you will see a glowing pipe next to the engine. The Ancient Weapon is stored inside this pipe.. but we have no way of cutting the pipe open. Remember this location for later. You will be able to quickly move back to the engine after unlocking all of the gates in the dungeon while completing the area.
When you come to the town of Vestyrka, you can speak to a man who lives in one of the north-western houses. He is the mining supervisor, and has plenty of extra saws on hand. He offers to give Melrose one, if you have talked to the woman in the house east of his who asks you to help cut open her kitchen sink pipe. After obtaining the saw, you can help the woman in Vestyrka. Of course, more importantly, it can now be used to cut the pipe at the Love Engine.
Teleport back to Valentown, and return to the Sweet Tower. From the Memory Teleportal in Valentown, you'll have to go north to the world map to get to the Lands of Love. Navigate north through here to get to the Sweet Tower. At the Sweet Tower, go down the ladder into the Love Dungeon. Go south down the stairs and enter the first shortcut door to the east. When you come out this door, you will see a switch to the east. Snack along the path to the west and go north at the first opportunity to get to the Love Engine (the same room with all the puzzles and the Memory Orb). Interact with the pipe... and voila! You can now equip Christina with this awesomely powered up weapon and get the achievement.