Hydras are a pain- I run them often enough, I should know- so how do I like to put down a 5 headed chicken?
1: Flame banner on a fairly large group of Saurus. Cheapest painful charge in the games because it's just a small Core group, plus 10 points. It won't have great long term CR, either. Just beware if it lives for longer than 2 rounds as that will be over-extending yourself.
2: Do your best to nail it with a Lore, or synergy with a group to do it- You can't hit the handlers (it's a special rule they have, so watch out for canny players who know that) but you can nail it to a wall if you can figure a way to buff skinks or something unexpected to just take it out.
3: Salamander. I only know 3 Lizzie players, and I know at least one or 2 that carry 2 Sala's regularly. You may not get the panic text, but any wound you can get that it can't regenerate is awesome because it's S starts @ 5, and lowers per wound.
I'd dispute the ASF thing quite a bit. Being a mainly Druchii player, and trying to kill those HE jerks MANY times and failing half of them(lol), it just affects normal combat. If you have ASF banners on something it just becomes a matter of Initative buffs if you could give it to your unit.
and no: Repeater CrossBows DO get the -1 for DTap (also for Musician Reform, and another for long range after 12") .Repeater Bolt Throwers are a machine of an entirely different calibre lol; they only get 2 types of shots 1 big one that mows rows(Ignores Armour, D3 wounds, and -1S for every row you keep going thru), and a barrage of 6 into one guy(-2 Armour plus Strength penalty to Armour).