Tomb Kings are probably about as powerful as we are, and depending on how good his composition is, you can smash them pretty convincingly;
Hierophant: They moan about it, but it only slightly weakens them when he dies, so don't think it's over, they can still eat you with other magic and monsters. That said, he is likely to be the only source of regen magic for them, as its a terrible army lore they are saddled with (a fate we may share come next year). I'd send in a Scar-Vet with a good 'Steed of Shadows' cast, you only need a halberd to kill him, Burning Blade is hilarious overkill and you can probably murder the Tomb King/BSB whilst you are there. If you really hate your opponent and want him to cry like a girl, on Turn 1 use the Blood Statuette on your Skink Priest to snipe the Hierophant. Don't even need 'Withering', he's already T3 so very easy to kill.
Tomb King: WS7 for everyone! Buff your Scar-Vet missile with 'Speed' or 'Timewarp' before launching him, run in and hack him to death with flaming attacks. The curse will kill you in return, but thats cool, you've only spent a fraction of his points to murder him so meh
BSB: He can fight, but only two wounds, and you are faster (especially with 'Speed' up), so just kill him before he rolls for 'Killing Blow'
Skeletons: If he brings combat blocks, laugh and smash them to pieces with your Saurus and magic. If he brings archers, use EOTG and 'Pha's Protection' from your Light Slann to screw up his shooting phase, 'Iceshard Blizzard' from your Skink Priest is also handy if he takes a giant unit with Khalida (why can't I hold all these misses?). You'll have to march through all the arrow fire to reach him, but the result will be the same, you'll still smash them apart pretty easily.
Chariots: They're intensely annoying and highly effective, careful deployment and casting 'Banishment' and 'Burning Gaze' into them should take off a few wounds before they hit your lines. Tying them up with Skink skirmishers is pretty good too, buys you time to pull in the phalanx so they have to charge your front rank regardless.
Monsters: They are all T8 and I2 (the big ones I mean), so 'Pit' is enough to kill them (and with only D6 scatter, you can cast the smaller one easier and more accurately, as they are such huge models, it takes horrible scatter to miss). If they actually hit your combat blocks, 'Mindrazor' will end them.
Snake Surfers and Stalkers: They're fun, but so expensive so you are unlikely to see many. Again, 'Pit' will hit enough models with the small blast to murder them, and they lack staying power in combat when you throw down 'Mindrazor'.
Casket of Souls: Annoying, but it is a spell casting so just block it with your Slann's dispel, it is pretty easy to shut down (just like the laser cannon of the Empire). We have awesome Leadership, so it's not really something to overly worry about, and it'll die once you hit his lines anyway.
They are not like Vamps, they can't regen infantry to anywhere near the same degree, and their offensive magic boils down to Death sniper spells (Purple Sun, if they bring Arkhan) and Light spells (which our infantry are pretty resiliant against, EOTG, and Light gun magic is easy to dispel). He can still gank your infantry blocks with multi-charges (ie tying up the front rank with cheap Skeletons whilst Chariots or Snake Surfers charge into the flank), so a tight phalanx marching into his lines is a good plan, and Skinks are good for delaying his charges.