Titan Core is a relic piece obtained by defeating the Titan, the 2nd Boss in the Cavern of Ancient Ruins. Alternatively, you can purchase it from the Adventure Store for 400 Smith Tokens once you have obtained 4-Star Mastery in the Cavern of Ancient Ruins.
The other pieces you need to create Titan Castle Crusher are the 3 Rank-A Obsidian Swords; Fleet Slicer, The Black Blade, and Cell Divider. As you can see in the below picture, it will tell you how many correct swords you have. The below picture has none with a gold border, so it still needs all 3 Rank-A swords.
Successfully fusing the 4 components together for 36 hours will result in your sword.