Imo main issue is, that you dont have any champ with AoE HP burn listed here. HP burn is super powerful on spider. From what you have listed here. My guess would be

 Armiger - for turn meter control (prioritize Speed, Crit chance , acc )

Miscreated Monster - for Shields and spiderling control (prioritize HP and acc)

Psylar - use her as your tank, put her in lifesteal gear with giantslayer mastery. Build her with +-4k defense and at least 250 resistance. She also needs to have the lowest HP in your team. I would recomment around 35k for spider 20) + she has accuracy decrease debuff which is super useful for spiderlings and aoe decrease speed ( if your Valkyrie is fast enough, dont build speed on Psylar to have permanent retaliation up and you wont need Monster in the roster so you can swap for someone else)

Coldheart - turn meter drop and a massive damage that cant sort of substitute for lack of HP burn

Valkyrie - puts retaliation on everyone making sure your psylar doesnt die. 

This team will definitely not be the fastest, but I think it will be able to beat spider 20.

Note: I have built this team based on spider 20 which is spirit affinity. On 18 or 19 Psylar might not work as a tank because of the affinity of other champs and they will be targeted instead.

My personal roster for Spider 20 is this (in case you have any of these champs but didnt list them here) - Armiger, Psylar, Drexthar (tank), Tomb Lord, Apothecary

Imo main issue is, that you dont have any champ with AoE HP burn listed here. HP burn is super powerful on spider. From what you have listed here. My guess would be

 Armiger - for turn meter control (prioritize Speed, Crit chance , acc )

Miscreated Monster - for Shields and spiderling control (prioritize HP and acc)

Psylar - use her as your tank, put her in lifesteal gear with giantslayer mastery. Build her with +-4k defense and at least 250 resistance. She also needs to have the lowest HP in your team. I would recomment around 35k for spider 20) + she has accuracy decrease debuff which is super useful for spiderlings and aoe decrease speed ( if your Valkyrie is fast enough, dont build speed on Psylar to have permanent retaliation up and you wont need Monster in the roster so you can swap for someone else)

Coldheart - turn meter drop and a massive damage that cant sort of substitute for lack of HP burn

Valkyrie - puts retaliation on everyone making sure your psylar doesnt die. 

This team will definitely not be the fastest, but I think it will be able to beat spider 20.

Note: I have built this team based on spider 20 which is spirit affinity. On 18 or 19 Psylar might not work as a tank because of the affinity of other champs and they will be targeted instead.

My personal roster for Spider 20 is this (in case you have any of these champs but didnt list them here) - Armiger, Psylar, Drexthar (tank), Tomb Lord, Apothecary