I'm going to have to give up without finishing most likely, spent 7.5 hours trying to beat the boss at the end of heaven dungeon and I'm not getting any closer. It's ridiculously hard.
Its pretty easy when you have a plan. Teddie should have party buff spells, party attack raising spells, and spells that deplete Kunino Sagiri's defence. Use them all, and re-buff as soon as they finish. Yukiko has party healing spells and a feckload of MP, so she is your designated healer when its needed, or else she can attack as well. Your MC and Yosuke (who I had as my other member) are the main damage dealers, use mind charge and your -dyne spells (agidyne, ziodyne etc) to do maximum damage.
At some point Kunino Sagiri will use quad converge, which will mean he is using only one element and his defence is raised against all other elements. When he does this, whichever element he chooses to attack with will also be the element he is weak against, so just have your MC switch personas to one that has strong spells with and strong defence against that particular element, and have the rest of the team guard each round so that he does minimal damage to them. Sometimes he'll choose an element that is also a strength for another team member (like fire, which Yukiko is strong against) and there'll be no need to guard, because the attack wont inflict too much damage and you can have two characters hitting powerful -dyne spells against his while his defence to those spells are down. Just make sure you heal when the quad converge is finished, and use Teddie to use his buff/drain magics again.
Then he'll take control of one/all of your party members, and they may be used to attack you, or they may just end up doing nothing if you get lucky. I think they only ever get used to do physical damage anyway (dont hold me to that), so you can switch to a persona with high physical resistance and they'll do little damage. Eventually they will come back to you and you dont want to have to use too much healing magic/items unnecessarily, so carry on attacking Kunino Sagiri the same as you have been doing.
Towards the end of the battle Kunino Sagiri will start using Unerring Justice, which will deal heavy damage to all of your characters. The good news though is that he only does this when he has around 1000hp left so you know you're close to the end.
Its more a long battle than a tough one, you just have to remember that at best you can attack with 3 people, and if there are rounds where you have to guard with everyone in order to give your healer a chance to heal you all, then do it. And dont forget that if you switch personas on your MC he can also be used as a secondary healer if needed
I dont know what personas you have. I used Black Frost, Trumpeter and Thor for the last 4-5 dungeons, that was all I needed really. Black Frost in particular is a beast