Sylph Bowstring is an item that is used to upgrade Zael's crossbows. It is very common found via seeking in Lazulis City. But most can be found in dungeons dropped by enemies or found in treasure chests. They can be farmed in the Haunted Mansion. If I recall correct, in the area with Terracor, and right before you defeat it, there are two chests to the left of you. One of the chests contains 2 Sylph Bowstrings. Grab them before you kill Terracor, and just leave the dungeon and repeat.
There is a gold chest in the repeatable Sea Cave as well that contains 2 Sylph Bowstrings, found on the way after defeating the first group of Reptids.