If your HE opponent is bringing Tyrion vice Teclis, rejoice since he is unlikely to have a high level wizard as well since Tyrion is very expensive. A scar vet on a cold one with GW, dragon helm, dawnstone and the other trickster's shard should work. Tyrion has flaming attacks so between the AS re-roll and 2+ vs flaming the SV should survive. On the offensive side, the S7 attacks back forcing Tyrion to re-roll ward saves should allow a wound to get through per turn. To really make sure, get static combat res working in your favour as Tyrion is not stubborn and the easiest way to kill him is to run him down. Edit: as per later post, trickster's shard won't work since Tyrion has regen so replace with venom of the firefly frog.
I think Stegadon or Cold One Cavalry is a matter of personal preference. You probably don't want either to fight Tyrion directly. There's pretty much no non-character he can't ruthlessly butcher so you probably want to feed him cheap units. You probably want to tarpit Tyrion with a large unit of Skroxigor or Saurus enough to keep Steadfast. Because he's spending 400 points on fighting character, you'll probably have more units than him. Thus once tarpitted, you should have enough troops to flank Tyrion's unit (I'm guessing Dragon Knights). You should feed Tyrion unit champions via challenge to Tyrion to absorb his hits for you. Hopefully you should be able to kill enough rank and file elves to beat Tyrion's unit with combat resolution. Life or Light should tilt the overall combat in your favor with judicious use (pretty much any lore except Fire and Metal really). Since he probably won't be fielding a wizard lord, you should be able to dominate the magic phase. If you really are itching to beat Tyrion by killing him and not bypassing him, I would recommend a Scar Veteran or Oldblood equipped with the Dragonhelm or Dragonbane Gem would do okay giving you a 2+ ward save versus every hit they suffer. Then give them great weapons to knock Tyrion's save down a notch. The Lore of Death supplemented by the Blood Statuette of Spite could take him out early, but Tyrion moves so fast you are likely only to get one round where you can hit him with a direct damage spell before he's reached your mainline.
Doesn't work since Tyrion has dragon armour that grants 2+ save vs flaming attacks. @ Durandal: Just read the HE book and you are spot on, Tyrion has both a ward and regen save (from back in the day when you could use both) so trickster's shard won't work. On the positive side, it frees up points to take VoFF to autowound with poison which will help avoid those nasty 1's to wound!!