There are many things that make this fight complicated.
The worst is his brand:
-healing: don't. heal. your. pet. Reall. It will regenerate him too quickly. To keep your pet alive, you must use T5 (not affected by his brand). And of course, take a ferocity soloing-specced pet for his self-heal and, if needed, heart of the phoenix. I don't know if you can survive the fight without chimaera shot healing you.
-damage: don't damage him when you have the brand, except with serpent sting. Personal damage isn't too important, i'll explain later. On the good side, it shortens the fight. On the bad side, your pet will be in passive for the fight (except a small window in the beginning to mount aggro). One thing to keep in mind is that he will not cast it on his target. So if you taunt him just before your brand expires, you will have 8 seconds of pure dps (but no kill command, remember, your pet is on passive). But it will probably be luck, since stopping him from tearing up your pet will normally get you taunting non-stop.
THE ICE PATCHES:
Key to this fight. You see, Tyrannus runs really fast. But the ice slows him down a lot. So you must position your pet on one side of the ice patch, and stand on the other, and taunt, taunt and taunt. If done correctly, Tyrannus wont get a single hit on either of you.
Just change ice patch once in a while.
Secondly, the ice patch is something like 3K dps, wich is pur luck, since your dps will be very low (espacially in BM). When i soloed him, i did only 50% of his hp, the ice did the rest.
Finally, you got the freezes. They are bad. Worst scenarios: you taunt, but you are too near the boss: he hit for 20K, once gave me a 44K. Or your taunt finishes, your pet gets a beating (CD!). Or your taunt finishes, Tyrannus enrages, gets 6 seconds on your pet, kills him without remorse.
So everything is in the taunting and positioning. Taunt him when he's on the other side of the ice patch, but don't wait too long if you're going to get frozen, keep your pet alive without mending... Phew, he was hard. Better have patience. I did it in blue gear 333/346 (and T5), so it's more skill than equipment. Reserved for motivated soloers.