//Short version
Protect your party against Water (or Wind, but preferably Water) using Typhoon Ring, Adaman Bangle, Elemental Materia, or Chocofeather. Bolt Armlet + Aurora Armlet can also block a couple of attacks. Materia like Osmose, Heal, etc. have elements like Water, Wind on them for use with Elemental Materia.
Get Barrier up and avoid using Haste. Focus down right-head first with a spellcaster, the other two party members focusing support (one of these supports should be geared heavily for physical attacks to kill the left-head later).
Avoid using attacks that hit both heads like Summons as they both have a counter-attack that triggers when attacked enough times. Focus on the right-head, and when it dies, left-head will become more aggressive but be less dangerous due to your elemental protection.
Watch out for final attacks from the heads when they die, make sure you're healed up and use Sense to track HP.
***
//Long version
The right-head is physical-aligned, and the left-head is magic-aligned; they are immune to damage of their aligned type. Right-head uses mostly physical element attacks, whereas left-head uses a mix of Water, Wind, and Ice. Water is by far the most effective element to protect against in this fight, as Left's standard attack and variant of the Double Attack are both water element. If you have the Typhoon ring from outside the Forgotten City (used to be Water Ring), or an Adaman Bangle then those will be handy here. Otherwise, Elemental + Osmose, or Elemental + Leviathan can reduce the damage Left deals.
Both heads, like the original Schizo fight, have a counter-attack which triggers when the heads have been attacked a certain number of times.
Because of the physical immunity on right-head and the magical immunity on left-head, it likely isn't possible to damage both heads at the same time. So try and avoid using attacks that hit both heads at the same time as you'll increment both their counters and may accidentally trigger both at the same time.
Right-head: After being hit 5 times, will use Tremor (Physical, removes protective magic)
Left-head: After being hit 6 times, will use Avalanche (Magical, ice element, inflicts Slow)
As Left-head's counter is Ice element, an Aurora Armlet can be handy for that (though like I said above, Water is the better element to protect against; Ice protection would be a nice bonus).
This set up with the counters means that it can be dangerous to bring both heads down at the same time, but when one head dies the remaining head becomes more aggressive and starts using stronger attacks. That can usually throw people off the first time.
And when one of the heads dies, it uses a unique death counter; right-head uses a final attack that can inflict Poison + Darkness (100% chance), while the left-side head uses a final attack that inflicts Poison + Silence instead (but at 33% chance. When the last remaining head dies, it uses a stronger version of the final attack (left-side's final counter when it is the last remaining head is Bolt-element).
Now for beating this guy. Both heads are weak to Earth, and the left-side head's attacks can be reasonably defended against using equipment like Ice Ring/Aurora Armlet (Avalanche counter-attack is Ice element), Typhoon Ring/Adaman Bangle (his standard single-target attacks are wind + water element), and Bolt Ring/Bolt Armlet (his final death counter as the last remaining head is bolt element).
The right-side head, though, mostly uses physical elements which are harder to nullify. So I reckon it'd be a good shout to prepare your team to block Water (this will counteract left-head's beam attack, and his variant of the Double Attack which is water element). Focus on killing the right-side/physical head first with Quake or Quake2 if you have it. Play it safe with one caster doing the damage, and the other two focusing on support (have one of these supports geared up for dealing physical damage, as you'll need that for the left-side head once the right-side head is killed).
If you have fairly decent coverage of Water-element protection, you can maybe forgo MBarrier and focus on maintaining Barrier instead. If you don't have good access to elemental protection then keep both up and avoid using Haste as it will drain them out faster (Wait ATB as well, Active ATB makes barriers almost useless).
When one of the heads dies, the other head becomes more aggressive, which can be dangerous due to the heads using a final counter when killed. Use Sense on the right-head so you can keep track of its HP (19,000 per head) and top your mitigation/HP up before landing the killing blow, with a turn or two on standby to heal up the damage. Land the finishing blow on it when your party is in a fairly stable position.
With right-head dead, you'll be dealing with left-head and his elemental attacks. Typhoon Ring will halve the damage his attacks deal, but Adaman Bangles or a Lv.2 Elemental paired with a water-element Materia will outright negate them. Wind can also be used to block Left's standard attacks if you're stuck for Water options (a Choco-Feather nulls Wind for instance) as these attacks are dual-element; Water + Wind, blocking either one will block the entire attack.
Left-head also uses a final attack when it dies (bolt element when it is the last head remaining), so make sure you're topped up before finishing him off.