Fun fact, I have every lego for a while but this is first raid where I actually have enough gear to play all 3 spec's and can swap depending on fight.
Here are the tips I have so feel free to add up. Spec about fire spec since I don't play fire that much and might be blind to some nice things.
Mythic Garothi
Best spec here is frost simply due to fact you can use 2 ice blocks in last phase while soaking.
In case you didn't know if you use ice block while soaking you wont get kicked from pool so frost mage can take care of soaking one pool alone.
Mythic Hounds
Damage wise frost should be superior to arcane or fire if you stack them first 10 sec and cause we can use double bloodlust in this fight.
If you can use double icelance frost is clear winner here.
Mythic High Command
Arcane is clear winner here.
Fire is good choice if you're progressing and your healers are struggling simply cause with fire you can stay back while arcane must be closer, aka they tend to get hit more with ww, charges and stray bombs.
But where arcane shine is killing bats. There is no spec in my guild that can come even close to my bats damage.
Closest ones are druids and they are always like 50-100 mill behind me at the end of fight.
Arcane aoe burst is simply to strong and valuable for this fight.
Fire will do good aoe damage as well but not as fast, and speed is priority here.
Frost is weakest here, it is safe as fire but fire has more aoe damage.
Mythic Hasabal
Arcane wins here.
Arcane burst is very usefull for fast kiling the imps bottom or killing minibosses top.
Just be sure to save your burst cd's for them and not using them on pull
Frost can be very strong for miniboses as well, not so much for imps.
In my guild no druid,lock or warrior can come close to my imp damage while I play arcane.
Mythic Eonar
This is annoying one for me.
While I do huge arcane damage when alive I died almost every time here cause of green debuff (yea our healers suck)
I even wear prydaz, use every def cd and green debuff kills me.
Arcane has good aoe+slow with decent ST on miniboses.
Frost looks good with its good ST and slow on trash but weakest spec here I think.
Now fire looks very strong if you have to pick green debuff like me.
With prydaz+healing shimmer+cauterize and solid AOE this looks like a spec to pick if you are strugling to survive like me.
You don't have slow but at least you are not dead ^^
Mytic Imonar
I would say arcane wins here for me.
Your burst cd's will be spent on boss , while on downtime you will be crosing the bridge anyway, eliminating your weak point.
First crossing is easy so no def cd's should be used.
Ice block should be saved if you ever get touched by a ball to clear that nasty debuff.
For other high damage (aka crossing bridge second time while tanks are procing lasers and bombs) great invisi should be enough.
Frost has its uses with double iceblock but damage wise arcane is better.
Haven't tried fire here.
That's all from me, haven't killed more than this on mythic, so other ppl continue with tips and ideas