The ingredients for the Hatching Enzymes are easily gathered by reactivating and using the four Alien Arches in the Primary Containment Facility. The arches lead to the Lost River Ghost Forest (Ghost Weed), the Crag Field (Eye Stalk), the Mushroom Forest (Fungal Sample) and the Bulb Zone (Bulb Bush). Sea Crown can be found in the trenches of the Sea Emperor Leviathan's aquarium.
Data Bank Entry
In a normal life cycle it seems emperor specimens would have buried their eggs in much shallower waters, where different organic materials in the soil would have triggered a hatching response.
By combining flora from the emperor's nesting regions with a hatching enzyme from the parent itself it should be possible to fabricate a substance which would synthesize the natural environment and catalyze the birthing process.