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Patience first and foremost. Never, under any circumstance, should you face the both of them simultaneously. And never, under and circumstances, should you continue the fight with one WHILE RAGED if another one enters the area. Focus on one at a time, and use the proper strategy against whichever you've engaged.

"Proper strategy?" you may ask. Well, lemmie break down some simple pointers for any weapon-type.

Rathian: Queen of the Earth. Don't expect an aerial battle and, for that matter, don't expect to stay in front of her for more than 2 hits and NOT get hit. She does, however, possess a major weakness: her legs. Tripping her is far easier than tripping Mr. Rathalos. Oh, and if she decides to flip, never rush in unless you're certain she's done or she does 2. And never go for the head after those flips because she usually follows into her next attack quickly. She may even blindly charge forward without homing on you.

Rathalos: Me and this guy go way back to MH1. His domain is the sky (which he can be shot/flashbombed out of if done correctly). He's got strong legs, so don't try to focus too much on them unless it's his only open target of his body. His head is his weak point (so is the Rathian's, but their openings differ. Rathian is best weak-shotted when tripped and after triple fireballs, Rathalos is best weak-shotted when doing a single fireball or RIGHT after getting knocked out the sky).

And seeing how this fight will take you a half hour, roughly, come prepared. 10 herbs, 10 potions, 10 mega potions, 3 Lifepowders, a good number of paintballs AND whetstones (or ammo, if you gun it up), and your best defense and/or fire resistant armor.

dude if you wanna get it done quick just bring

5 flash bombs
flash bugs and that other things that makes them ( bomb materiel or gun powder)
shock traps
potions
mega potions and all that stuff.
just equip a good hammer use flash bombs on them and just hammer their heads. do this until they die

it's pretty easy just bring a weapon with like dragon element or the all amazing onslaught hammer and keep 'em seperated while you make them regret being born it's pretty simple just avoid attacks and aim for the head as much as possible but make sure if you're using a blade type weapon you cut the tails off first cus they're really annoying and you might get a los or ian plate

If you can kill a rathian, and you can kill a rathalos, you can kill them both together. Don't fight them both at once, though. Leave if the other shows up and focus on one at a time. I like taking down the rathian first because I find rathian easier to kill. Then you're alone with the rathalos. If time is the culprit, make sure to bring plenty of paintballs to keep track of them at all times, flash bombs to blind them, traps to capture them or just wail on them, etc. If you keep dying, bring two books of combos, 10 potions, 10 mega potions, 10 herbs, 10 blue mushrooms, and 10 honeys, that way in theory you have access to 10 more potions and 10 more mega potions, though you need to sacrifice a regular potion to make the mega potion. Bring any other restoratives you have, as well as demon drug and armorskin or even armorcharm and demoncharm if you can afford them. Oh yeah, and a few max potions/ancient potion to max out your health levels before taking them on.

The problem with suggesting weapons and armor is that if you're not passed the village chief's five star quests and into the six star ones, you probably aren't at a high hunter rank and I doubt you'd have the materials to make a weapon with a dragon attribute or have a full set of Kirin armor, although you can take the Kirin on before the Troublesome Pair quest.