BUT... THEY ALL STRIKE FIRST!

ep, that's the first thing most people notice about the High Elves. Every High Elf (not including their mounts) benefits from the Always Strikes First special rule. This, as you might expect, gives the warriors of Ulthuan something of an advantage over their previous rules. That said, it doesn't make them unbeatable – not by any stretch of the imagination. Rather, what it does is cause anyone hoping to defeat them to look at new and interesting ways to do so.
For a start, don't charge the High Elves to the front unless you are sure your unit is up to the task. Gone are the days when Skaven Slaves, Night Goblins or Empire Free Company could charge a unit of High Elf infantry to the fore and laugh off the consequences. Now, any such frippery is likely to result in blood and pain.
Instead, look for ways to reduce the Elves' strengths. Take them on the flanks if you can, or, better yet, come up with ways to get around their Always Strikes First advantage. Ways to do this include: shooting them, running them over with chariots, unleashing Fanatics into their ranks and casting spells at them (more on all of these later).
BUT, THEIR ELITE INFANTRY IS REALLY GOOD...
Yep, High Elf infantry is worth taking. In fact, I'd go so far as to say that it's among the very best in the game. That said, it's far from impervious. Let's break down the big three:
White Lions. Armed with great weapons for a stunning Strength 6 in combat, and Lion Cloaks to make them harder to kill with shooting, these stubborn soldiers are a scary proposition. That said, they only have 1 Attack each, and though they're strong, they aren't very good at receiving damage in return up close. Tackle them with your own infantry soldiers. Saurus Warriors, Savage Orc Boyz or even a good solid unit of Skaven Clanrats armed with Spears will weather the worst of a close combat and still strike back hard.
Don't feed them your Heavy Cavalry or elite troops (like Greatswords or Storm Vermin). The White Lions will chew them up and spit them out with their Strength 6 attacks.
Phoenix Guard. So much better than they used to be, the Phoenix Guard are incredibly durable with heavy armour and a 4+ Ward save. They can go up against some of the best hitters in the enemy force and keep on fighting. That said, they're the weakest of the Elite infantry, with "only" Strength 4, so they're not going to make that big a dent on your own heavier armoured troops. Ogre Bulls, Tree Kin, Minotaurs and Trolls have all got what it takes to deal with the Phoenix Guard and don't have to worry about their Cause Fear special rule.
Don't waste too much firepower or magic on the Phoenix Guard – they're well equipped to shrug it off, and don't send in units that they might outnumber. The last thing you want is to lose the combat and get broken by a Fear -causing enemy.

High Elf Sword Masters rush towards the Dark Elf battleline.
Sword Masters. As resilient as a paper towel, the Sword Masters of Hoeth are nonetheless among the hardest close combat troops in the game. Two Attacks at Strength 5 makes them utterly lethal, especially when combined with Always Striking First. The best advice against these fellows is simply not to fight them. Shoot them, magic them and run them over with chariots...but don't give them the satisfaction of fighting back.
Next:
But, They have a new Dragon, and it scares me...
Previous: Introduction

