When he limps just trap him and tranq him, you'll still complete the hunt even if you capture.
When you use great sword you should charge attack almost all the time, you probably won't get off charge lv3 on him too much though but lv1 or lv2 charge will do, mainly just run in a circle into him charge swing down, roll to the side sheath and run, then repeat. If you have critical draw that'll boost your damage immensly. I think my run with Rathalos is about 15-20min now, all depends on how much he keeps flying. You can also vertical swing below his shadow if he's kinda close to ground, I would run in and vertical swing on him, and sometimes he'll take a lot of damage and just fall onto the ground for a good 5 second, which is enough for a lv3 charge to cut his tail, break wings or head. Also, if you want since he does fly alot, bring flash bombs, if you can get a good lob anywhere in front of him while he's flying he'll fall down stunned, you can get off probably 2 lv3 charge and when he gets back up he'll most likely still be stunned for another lv 3 charge, just becareful he might start doing the tail whip spin so be ready to let charge early and roll away.
Oh you can block with your sword when he roars too, this is pretty useful because usually after the roar he'll firebomb in front of him.
If he charges you can also run behind him, to the right I think? and start a charge, he'll turn around and let go at lv2 or 3 charge and it'll slam on his face, this takes practice though...