So, the first time I fought midir, I spent at least 20 embers or so before defeating him. When I finally did defeat him, I snatched the Frayed Blade and felt good about myself. I then got into NG+2 and forgot to fight him, jumping to NG+3. Then, as we meet again at NG+3, I was able to defeat him after 3 tries. I was using the Black Iron Greatshield to defend myself against his fire breathing attacks, and the Wolf Knight greatsword to dish out the damage.
I continually attacked his head, dealing around 500 damage per swing. When I first fought him, I didn't care about hitting the head, instead attacking his legs. I was also pretty lucky, not getting disintegrated by his "IMMA FIRIN MAH LAZOR" attack. Am I good, has Midir become old and weak, did I fight him the proper way, or were I just plain lucky?