It is flanked by two 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.
Another, albeit MP/PE reliant, strategy to easily dispose of this creature is to negate all PE cast on/from it by pushing Eve back using Plasma (3MP per cast at Lv.3). This might get tricky, as its range is limited and Eve's got a shield up as well.
A very viable and useful strategy against the Puppet Stinger is to use Energy Shot with the Grenade Launcher or Grenade Pistol with Grenade ammo. This will quickly take out the Derangement Speakers and each subsequent shot to the Puppet Stinger will stagger it. If shot at a constant stream of grenade shots, the boss will essentially be stagger-locked and becomes the most menial of bosses in the game.
Lvl. 3 Energy Shot and normal grenade with Crystal Skull and Ofuda deals roughly 180 to 200 damage per shot, up to a staggering 380+ on its combustion startup where it drops its antibody effect.