Fain Would Lie Down

If you are soloing this and don't fully understand, as it isn't explained well here, in order to get him to mount up on a specific mount, just fight right at that mount to start the fight. He'll mount up on the animal you are closest to.

A reference to a 17th-century Scottish ballad titled "Lord Randall", where a young lord gradually reveals that he has been poisoned by his lover. Each stanza ends with the line that this achievement paraphrases (as the original spelling is more phonetic, i.e. "I fain wad lie doun").

Full text can be found here.

Unlike most other kill-order achievements, this one barely changes in difficulty when you change the order of the beasts you have the boss mount up. The boss only gets the beast abilities in a different order but the end phase remains the same no matter which order you choose to do.

Killing Cruelfang first:
This is the beast you have the boss mount up first when you do the encounter normally and is the easiest one to begin with. Once Cruelfang is defeated the boss gains Cruelfang's Swiftness allowing him to use Rend and Tear when he isn't mounted.
Ideal order: Cruelfang -> Ironcrusher -> Dreadwing

Killing Ironcrusher first:
Beginning with Ironcrusher is the medium difficulty order. After Ironcrushers death Darmac gains Fury of the Elekk which allows him to use Tantrum when he isn't mounted.
Ideal order: Ironcrusher -> Cruelfang -> Dreadwing

Killing Dreadwing first:
Starting the fight with Dreadwing is the most difficult order to start with. Killing Dreadwing gives Darmac Spirit of the Rylak which lets him use Superheated Shrapnel when he isn't mounted. It also causes the spears spawned by Pin Down to become empowered with Seeking Embers and the Pack Beasts that the boss summons with Call the Pack become empowered with Flame Infusion for the rest of the fight.
Ideal order: Dreadfang -> Cruelfang -> Ironcrusher