All of these dragons are the biggest from their franchises, the Archdragons Avizandum and Sol Regem and the Alpha Bewilderbeast from HTTYD.
Where it takes place: A snowy island in the middle of nowhere, where no one can interrupt them.
First, let's talk about their sizes, there is no official measurement for Avizandum and Sol Regem, but I would assume they are around 60 metres long and 35 metres tall? Very big, but not gigantic like the bewilderbeast, which is confirmed to be 160 metres long and have a wingspan of 45 metres, it's roughly 50 metres tall too.
Abilites and feats:
Sol Regem has a huge and devastating fire breath that can kill any human or elf instantly, it's definitely hotter than any normal Sun Dragon's fire, but he needs to recharge it every few minutes. Avizandum can summon lightning to strike down his enemies and can also withstand freezing temperatures which will be useful when fighting the Bewilderbeast.
Avizandum and Sol Regem are known to fly incredibly fastly (especially Avizandum because he is a sky dragon) while the Bewilderbeast we have never seen in flight but we know they're not very fast on land but decently fast in the water. One thing that plays into the Bewilderbeast's advantage is those giant tusks that he has that can kill another Bewilderbeast with one charge, these would be lethal if they landed on either of the Archdragons, but as said before their speed might stop that. Avizandum is known to take down armies by himself and can only be stopped by many mages using dark magic.
We know that Sol Regem was able to destroy an entire village easily and survived one of the most powerful dark magic attacks but at a cost. That cost was being blind which is a disadvantage in this fight (though it does have amazing other senses) but If Avizandum was fighting the Bewilderbeast he might hear the thunderbolts and the bewilderbeast roaring and get in the fight. One of the Archdragons best advantages is that they are more intelligent, they understand speech and are masters of battle tactics while the Bewilderbeast is more like a really powerful animal.
One of the Bewilderbeast's advantage in this fight would be its "frost breath" it can shoot out ice spikes and freezing temperatures from its mouth, it can create LITERAL islands with this attack just by freezing the water proving this attacks' quantity and power.
So who do you think would win, the storm summoning Avizandum teaming with the fire breathing Sol Regem or the enormous, frost breathing Bewilderbeast?