First off try and get focus, evasion, and handicraft on a set. Keep in mind that one of the problems with the second half of the fight comes from wind pressure and roars so either get armor skills to help (LG ear plugs are able to fit with the aforementioned skills) or change shaka dances to help with those two issues. Armor tier matters little as long as your willing to mine the armor spheres. As far as weapon, hammer needs to be a G rank or close to it as they are G rank monsters with reduced HP.
Next is go into the fight ready to take out I. Lagi and Brachy. Bring traps and every healing item you can along with the components to make more. Bring a far caster and mega dash juice as you will need a failsafe and run around without worrying about stam.
As stupid as is sounds the goal is to kill I. Lagi as fast as you can (just don't get greedy) so that when Azure and Brachy come in you can play "monkey in the middle". I was able to get past it by positioning myself where Azure was between me and Brachy and Brachy made him all squishy. Stay mobile and get in a shot when you can, look for when 1 or both monsters are tired and capitalize. Do what you can but seriously until Brachy kills Azure look at it as the highest stakes game of tag you have ever played. Keep in mind that once they start fighting each other they will disengage eventually so always place yourself where the are hitting each other.
Using this method I capped I. Lagi around 8min into the hunt (I use GL) and ran around like a headless chicken till Azure died around 15min later. Brachy fell down around 5min after that. But that's just the way I did it, I am not leet enough to take on both G rank Dios and Los in the same room with no assist.