Help me beat this Neochu

I've finished the storyline and am now finishing all the missions. Up to this point, there have been many battles that took a few tries, but never any battles that I felt I had to grind for. A few moments' thought, a carefully-crafted Paradigm deck, and a bespoke strategy have gotten me through every battle at the moment I encountered it.

I'm now in Titan's Trials, I've gone through one set of five battles, and now I'm on the last battle of another: E1, Mission 45, against a Neochu.

I cannot figure out how I can beat this thing — not without leaving and coming back WAY later, anyway. It's hard enough to survive to the halfway point of the battle, and once the bloody thing spawns his Picochus it's all over.

I've been using Fang – Lightning – Hope. Fang has around 15,000 HP, Lightning around 12,000, and Hope around 11,000. All my Physical and Earth defense accessories have been distributed among them in several configurations. All three characters are over halfway through Stage 10 of their primary role Crystaria (all the 30,000-CP crystals are lit up), and Lightning and Hope each have Stage 1 of Sentinel.

I begin by Hasting everyone, then immediately switch to COM – COM – MED. I always have to have a Medic, because if I don't, two consecutive regular attacks can kill a party member.

This continues until Neochu is about to Screech, at which point I switch to SEN – SEN – SEN, which is pretty much necessary to survive the attack. I then switch to COM – MED – MED or SAB – MED – MED to heal while keeping the chain gauge (barely) up.

Then the Neochu uses Pollen, so I have to keep my two Medics for a moment, then try to reHaste everyone, which is tricky because Lightning is not a good Medic and by this time the Neochu is attacking again! So I have to go back to COM – COM – MED which leaves me with several debuffs on each character, which are barely gone before the stupid thing Screeches again.

Thus I can limp along until the Neochu is at half health. Then he summons his Picochus. Then he screeches, making me pull out SEN – SEN – SEN. If I survive that, I can go SEN – COM – MED, but I can hardly get them all Provoked before my party members start falling, and even if I do, I can't then get Mediguarded in time to survive their initial onslaught.

What am I doing wrong? None of the strategies I've read elsewhere seem to indicate that I should be having this much of a problem just keeping everyone alive.

TL;DR: Help me exact vengeance on this accursed beast.