The key thing for Nether Spider is debuff removal or prevention. I personally use Reliquary Tender for that, which is a rare champ so easy to book.

I can't tell from your champs since I'm no good at recognizing pictures, but basically, you want either block debuffs or debuff removal, so that you can get rid of the poisons that get applied when it summons the pet spiders.

Bad el kazaar and Doompriest are good against Nether Spider

As others have mentioned, debuff removal is good, so BEK and DP. But also important is to keep the number of spiderling counterattacks to a minimum, because each counterattack will heal Agreth (in addition to putting another poison on your whole team). And of course the problem with BEK is that all of his attacks are AOE, so he'd constantly be provoking counterattacks.

Personally I just use AOE buff strip to remove their counterattack buffs, with my Sethallia or Serris, but I don't see too many good options for that in your roster (Hope has a chance to remove buffs also, but combined with an attack, so she'd first set off all the counterattacks before having a chance to remove them). 

So it might be better for you to try stunning the spiderlings instead, with Trunda. Vizier could also be good, to extend debuffs (like BEK's poisons) on Agreth and try to block both her healing and the ally protection that she gets when the spiderlings' counterattack buffs expire.