Idk why so many ppl complicates themselves when the fight itself is as simple as ds2's dragonrider bossfight (warning butthurts: SIMPLE and EASY are entirely different concepts). My strategy is the one that always ends up killing it, whether i'm a melee or a caster.
1rst, stick to the head and stay in front of him, because anywhere else takes x10 less damage from your attacks.
2nd. never roll towards him at melee range. Dodge backwards or to the sides depending on where his slashes and bites are coming from. Dodging towards him usually triggers it's fire breath and, while heavily telegraphed, it's something annoying to wait for.
3rd. The arena is huge, so don't mind about being pushed back repeatedly. Midir will eventually jump backwards if you re consisntent with your hits.
4rth it's second phase is almost skippable if you ve been hitting his head in the whole fight due to the huge damage midir takes from riposte. If he doesn't die from it, just rinse and repeat the previous steps.
Now, for certain attacks...
The charge attack the bossfight starts with: is highly detrimental for the boss as it will only position itself to your reach. If you dodge towards his fire breath and/or claws, you will end up behind him and you will have to chase him in order to deliver the first hits, so it's best to just wait for him and dodge hist last attacks to get the head faster. In phase 2 he will do this charge twice, so just dodge the first and wait there, he'll come back.
The downward fire breath (standing): As mentioned before, he will do this attack if you dodge towards him at melee range, wich will position you right under him. Run away to avoid the flames and make sure you re facing him when this attack ends, and keep smashing that jaw.
Tail sweep: This is the attack only those who refuse to learn won't be able to adapt to. And another reason why summoning is a bad idea. This attack is triggered by hitting midir's back side, whether it's the legs, the tail or the lower spine (where you SHOULD NOT HIT HIM). Not only your attacks will be practically useless there, but midir will retaliate with a tail swipe that covers a large amount of area, isn't so telegraphed as his other attacks and can easily one-shot you. With this attack, the game itself tells you that you' re doing it wrong.
Fire breath + dark beam: After the downward fire breath he does on four legs, a dark beam usually follows up. The timing to dodge this beam is the halo in the charging laser. When it disappears, midir will shoot the beam right towards you, so dodge sideways and keep away from that area to avoid the dark explosion from the beam's trails. An horizontal sweep with the dark beam will follow up this attack, so dodging backwards is recommended.
Dark explosion (2nd phase): Ok, this is ovbious as ****. You might have the time to give the head 1 or 2 hits, but don't take more risks and run away. Once the explosion is over you can go back to the hits.
Dark laser barrage (2nd phase): The startup of this phase is highly telegraphed. As usual, use the halo around the charging laser to time your dodge. After that, several horizontal and diagonal sweeps will follow, and these doesn't follow a certain pattern. They chase the are where you are at the moment, so roll backwards. You might risk to roll forwards as well, but that requires far better reflexes in order to not get caught by the delayed explosions. This attack ends with another forward laser sweep wich is the most damaging, so time your roll well. After this attack, midir will fall to the ground and he will be vulnerable for several seconds, so feel free to deplete your stamina bar on his head.
Important note: midir's general stats are off the scale, but health is the highest. So summoning for this fight is the dumbest idea if you re not an expert at this game.
That's about it, just some tips for certain attacks. The rest is easy peasy.