I've got a few words that involve countering a pyra.
Goldfish.
Manticore.
Burst rounds.
Chute Vent.
Phoenix Claw.
Port-side carronade.
Manticore.
In that order.
If that wasn't detailed enough for some of you, I'll expand a bit.
See a Gat/flack Pyra? Grab your trusty Disabler Goldfish and her forward Manticore. Throw a port-side carronade on her.
Tell your gunner to equip burst rounds. Go ahead and rush the Pyra. Make sure both your engies are on the hull, because it WILL go down.
When your gunner is in effective range, he'll shoot the burst Manticore, and disable the front guns. The enemy pilot will see his weapons down, but will likely still go in for the ram. When the Manticore is almost done wrecking everything, Chute Vent.
Ideally, the pyra will sail right over you. (I would not suggest Hydrogen to dodge the ram, because the enemy pilot may be able to match it. Chute Vents are rarer, because, to most pilots, down = bad.)
Slap on your Phoenix Claw and have one of your engies hop on that port side carronade. Do as much damage to the balloon/armor on the balloon as they can while you turn without the claw to spin your Manticore back around.
By this point, the Manticore should be done or almost done reloading, so cause havoc on their engines/port-side guns (depending on if they have the claw).
Congratulations! You now have a completely disabled Pyramidion! Your brawler ally can now finish him (if you haven't already) or you can take care of your own dirty work (if you aren't running a completely disabler Goldie).
The only trick is making sure that Gat doesn't take out your Manticore on the approach. I try to take as much damage with the balloon as I can. You're going to drop eventually anyway.
This strategy can be countered pretty easily by those who have mastered the Pyra, but if that pilot has got a 1-3 next to the wheel icon in the lobby, you can trust kills outta this one.