The Puppet Stinger is a massive Stinger class ANMC and one of the final bosses in Parasite Eve II. The most dangerous part of this fight is that it is flanked by 2 Derangement Speakers which slowly drain Aya's MP if they are not destroyed. Destroying these also cause the Puppet Stinger to recoil, cancelling its spells out.
A very viable and useful strategy against the Puppet Stinger is to use Energy Shot 3 with the Grenade Launcher. This will quickly take out the Derangement Speakers and then start to pound the Puppet Stinger. Overall it will take a large amount of grenades, around 20 with this set up so make sure everything is well stocked, especially for who shows up next: GOLEMs.