Welcome back & huge congrats on Ony, Ashes & Panther (I was lucky with Ony & Ashes - dropped the same month for me with Ashes showing up on my birthday of all days - and Ony being one of my grails, I was a happy girlie to say the least!).
If you were on US I'd offer to help you out with Malygos - but let me see if I can offer some advice, never solo'ed it on a hunter, but I've done it on my DK, Priest & feral druid. Main tips are:
I'm guessing just keeping aggro on your pet & keeping him healed is the main trick I can't help you with, but you want to burst down Malygos as quick as you can first phase - big hint here is when the sparks appear, you want to bring them down on the platform and then stand in them for the DPS buff (plus 50%). If Malygos gets it, then he basically gets that buff and hits a bit harder (again, not sure how that affects your pet).
Once he goes up in the air to fly around, then just kill the guys on the discs, then you fall through the platform and the rotation you must follow is:
1 - 1 - 2 -3 & repeat. Move out of the static things he throws at you, and KEEP. THAT. ROTATION. When you first mount on the dragons, get your 5 stacks of your heal (number 3), then start the rotation. Also - make sure you're not in melee range of him, fly out away from him so he can't melee you in the air - that saves you slapping extra damage.
With that - you'll never go low on health and as soon as he goes up in the air & the disc guys come down, you're basically guaranteed a win if you stick with the 1 - 1 - 2 -3 rotation. You will be waiting around most of the time waiting for enough energy to hit 2, but you need those stacks to stay on the boss to get him down
Best of luck with him!