WoWDB

Soloed Malygos 25-man Normal as level 90 Troll Fire Mage with average item level 544 (mostly from LFR, a couple pieces from Flex, one crafted BoE, and  Xing-Ho, Breath of Yu'lon). I have Tier 16 4-piece bonus and am fully gemmed, enchanted, and reforged. (calculator:talents and glyphs)

I did not use any buff foods - if your item level isn't as good as mine then I'd recommend doing this - but did use my ghetto flask,  Crystal of Insanity (15 minute CD). If you think there is a strong possibility of wiping, then bring along real flasks because  Visions of Insanity does not persist through death.

Phase 1:

First, cast  Ice Barrier and wait for it to come off cool-down (so once Malygos destroys it you can immediately re-buff). Put down a  Rune of Power modified by Glyph of Evocation. Use every DPS cool-down you have right at the start: Mirror Images (modified by  Charred Glyph), racial if applicable (I used troll  Berserking),  Kafa Press (if you have it), a potion of your choosing, and Time Warp. Living Bomb the boss and cast Fireball/Inferno Blast until Pyroblast! procs - wasn't hard for me to do with 42.09% crit chance - then use  Alter Time for a free pyroblast six seconds later. Get your Ignite DoT as high as possible within reason before using  Combustion (modified by  Charred Glyph).

Ignore the Power Sparks. They will buff Malygos' damage but it's more detrimental to you to kill them because you have his berserk timer to worry about.

Phase 2:

Malygos will fly out of range. Kill the closest Scion to you and hop aboard the hover disk. Fly around and kill all the other scions. The best way is to focus on one at a time, though it certainly doesn't hurt to DoT up any other adds in range. Just don't bother with direct AoE; it doesn't hit hard enough on them to be worth it.

Once the adds are dead, Malygos comes back into range. DPS him hard until he transitions to the next phase. Don't forget to use your RoP; the health regeneration is helpful.

Phase 3:

The floor breaks and you land on a red drake. Use vehicle button 3 (a HoT) five times just before Malygos finishes emoting and becomes targetable. This initial 5-stack is important, as it is essentially refreshed using the rotation below - and if it falls off you may be in a bit of trouble.

The key to killing Malygos in this phase is the Fire Breath. You must get up to at least 18 stacks. Use Fireball (button 1) two times, then WAIT for Fire Breath (button 2) to light up. Use Fire Breath then IMMEDIATELY use the HoT (button 3). You will never use button 4 or 5. While you are doing this, you will need to dodge the lightning balls. Remember! You can move up and down, not just side to side, so you will have plenty of room to avoid those lightning balls. Use your strafe buttons to move so you can keep the rotation going.

So your rotation will be: 1, 1, (wait) 2, (immediately) 3. Rinse and repeat. If you screw up the rotation, "keep calm and carry on." Just start your rotation over. (Though you are still working against a timer, so don't screw up too many times, ok?)

As Ideon says, it is possible for both mounts to drop.