Ecosynth Analyzers are acquired by dismantling Synathids caught through Fishing. Go to The Business in Fortuna, select the desired amount of Synathids available, and select the "Dismantle" option to extract the components. Each Synathid yields one Ecosynth Analyzer.
They can also be acquired as a drop from taking down an Exploiter Orb. Each loot yields 7-8 units.