Dont use AoE to spiderlings. Resist need 247. Enough HP and Defense. Thats the first approach. But can use many others. Such as sync to Demytha block damage to Agreth speed, when she turn and  spit his poisons.

Or another one strategy, remove debuff champions to remove poisons.

Your Bad-El that is currently highlighted has a total of 116 speed.  I am not sure what the gear is for the other champions but if they are similar then I think you might need to revisit them.  All of your champions should at least have boots with speed as their primary stat, but ideally they need to be in the range of 170+ to be competitive against content like this.

That said, assuming your gear is good, you have a number of champions that should be able to deal with this boss.  There are 2 strategies for beating Nether spider.  The first is to use heavy nukers to keep the spiderlings down, while the second is to simply ignore the spiderlings entirely.  The latter is the safer one that works best for hard DT and what I would recommend for you now.

Now, when I say ignore the spiderlings completely, I mean literally ignore them.  Do not attack them with anything, whether it be AOE or single attacks.  If you plan on running an auto team, then turn off all AOE attacks from the champions.  Yes, the spiderlings will attack every now and then but it doesn't matter.  

From there, pick champions that are magic affinity (or spirit, but avoid force) and have really good sustain skills, such as healing, resurrection, debuff cleanses, etc.  A sample team I would run would be:

• Scyl - Magic affinity.  A1 decrease speed for Agreth, passive healing each round.  Resurrect if required.  Turn off AoE
• Duchess - Group healing and Veil for added survivability, plus reduces damage to the team.  Also brings resurrect.
• Tyrant - Magic affinity.  Ally protect, which massively reduces the damage that all other champions take when Agreth uses his tide of toxins passive to attack and trigger the damage of all poisons at the start of the turn.  I use him in my team and this is the only thing he is bringing to the table, though if you can get HP burn onto Agreth then he will also reduce the inbound damage.
• Demytha - Void affinity, group healing.  Also brings block damage that can dramatically reduce damage taken if it pops at the right time

One of the biggest gaps in champions that I can see in your roster is actually a debuff cleanser.  If you had a doompriest then I'd take her to 50 and bring her in.  The healing and debuff removal every turn will also dramatically increase survivability.  Reliquary Tender is another great example of a cleanser that can make this fight significantly easier.

Avoid champions that have random attacks, such as Apo and Ninja.  These can hit the spiderlings and risk a counterattack, which then heals the boss.  The goal is to just take a team slowly wittle the boss down with single attacks, while healing and sustaining all of the inbound damage.  All of the above mentioned champions should have high HP and defense anyway.

Rose nailed it, including the gear on BEK. 

That said, I don't hate Ninja but you do need to turn off the A2 on auto. 

On another note: looking at just this page in your roster, I count 19 60s and 41 50s. Considering there's another 146 champions that aren't in your vault, I assume there's more 50s than that. You really need to be focusing on 60'ing champs so they can be fully impactful in later game content - like Doom Tower. 

I'm not sure if the other posters are suggesting you use BEK for this but - *don't*. You cannot use BEK on Nether Spider unless you are *sure* you can clear the spiderlings, because his A1 will constantly trigger the heals.

My suggestion:

• Geomancer (big counter damage to the boss)
• Scyl (passive healing)
• Duchess (just overall amazing)
• Aniri (helps your passive healers)
• Shamael (infinite counterattacks on the boss)

No, was just +1'ing that the gear choices on BEK look troublesome. 

I beat it with Liliitu,Raglin, Geomancer, Arbiter and can't remember the fifth. Spider killed herself on geomancer reflect.

You should try with Lilitu, BEK, Geomancer, Scyl and then either Shamael, Ninja (need to manual), Godseeker, Sepulcher (block debuffs).