One thing I've had great success with is taking a unit of 30 archers, instead of two units of 15. It does minimize your flexibility, but I play with High Magic, and casting Hand of Glory on that one single unit makes it great at thinning down units of anything that's T3, or clearing chaff units more reliably. Usually my opponents are more worried about Fiery Convocation or Walk Between Worlds so they let it go undispelled. In a pinch, I've also been able to tie up much stronger units by reforming 30 archers into six ranks of five models to help them stay Steadfast. Their stats are still good against other basic infantry like Clanrats or Imperial State Troops.
With 30 archers, I think you could lose the Sisters, and beef up your Phoenix Guard unit. I always run 20 (I try to stay away from 30, or 40 or more so my opponent doesn't hate me. Trust me, 20 will have plenty of staying power if you deploy them and use them properly). I would also put the Razor Standard on them to make them better against armored units.
Same with your two units of Spearmen, I'd probably combine them to make a unit of 40. I usually run 30 with the Banner of Eternal Flame.
You may want to put your BSB on a barded mount, and embed them with your Silver Helms, which I assume are were your Archmage and Tyrion are going. You'll want to give them all the defense you can. I'd scrap the prince if you're going to run Tyrion, or vice versa. You can build a really well armored prince for cheaper, but I'm all for including characters in High Elves lists because nobody ever runs them because of their points costs. Either way, you probably don't need two fighty characters, the points you save by eliminating one could help you put a ward save on your wizard, and the Book of Hoeth, and maybe leave enough so you can reintroduce the Sisters.
Are these the only models available to you, or do you have other stuff like Ellyrian Reavers, Eagles, Swordmasters, White Lions, chariots, bolt throwers, etc.?
Maybe something like this:
++ End Times (High Elves - Army Book (2013-4) -V8.8.0.) [2,500pts] +++ Uncategorised +- Army Size: Army (0-2999 points)
+ Lords +Archmage [347pts]: Lore of Life, Wizard Level 4
. Ithilmar Barded Elven Steed
. Magic Items: AB - Book of Hoeth, BRB - Talisman of Preservation
Tyrion [410pts]: AB - Dragon Armour of Aenarion, AB - Heart of Avalorn, AB - Sunfang
+ Heroes +Noble [178pts]: Dragon Armour, Lance, Shield
. Battle Standard Bearer: AB - Banner of the World Dragon
. Ithilmar Barded Elven Steed
+ Core +Archers [310pts]: 30x Archer, Musician
Ellyrian Reavers [80pts]. 5x Ellyrian Reaver: 5x Spear (Mounted)
Silver Helms [260pts]: Champion, Musician, Standard Bearer
. 10x Silver Helm: 10x Shields
Spearmen [400pts]: 40x Spearman
. Champion
. Musician
. Standard Bearer: BRB - Banner of Eternal Flame
+ Rare +Sisters of Avelorn [140pts]: 10x Sister of Avelorn
+ Special +Phoenix Guard [375pts]: 20x Phoenix Guard
. Champion
. Musician
. Standard Bearer: BRB - Razor Standard
++ Total: [2,500pts] ++Created with
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