Trips is definitely right about you having way too many 50s and not enough 60s... but as for Nether Spider, there are really two key points to that fight. One, surviving the endless stream of poisons, which requires a lot of cleanse and healing. And two, taking down the big spider without her getting constantly healed by the spiderlings' counterattacks (which also add more poisons), which means you need the spiderlings either dead, or CCed, or at least stripped of their counterattack buff.
That means Doompriest will be a lock for her passive cleanse/heal. Rae is probably your best bet to handle the little spiders, what with her move that has a chance to freeze them and removes their counterattack buffs. Scyl's constant healing should help as well - her AOE stun has potential but too low chance to apply, she'd probably provoke a bunch of spiderling counterattacks. Draco for his debuffs - but make sure he doesn't use his A2 until the spiderlings' counterattack buffs are stripped. For the fifth, there's a bunch of options - like maybe Ghrush, or Duchess, or others.
Duchess (lead) -- guessing you lack speed based on visix stats shown
Doompriest (level to 60 does not need books)
Drexthar (have you been buying fragments, you can actually leave at 50! lol)
Scyl (60 - does not need books)
lugan
I just realized, this question is for normal level doom probably. So I am thinking you have major gearing problems. Guess is you don't have many champs well geared with all those 50s. You should clear normal and move on to hard by swapping gear onto the right champs.