The key with Agreth is strategy, of which there are two approaches. The first is brute force which is to essentially kill the spiderlings and everyone when they spawn, while the second is to focus entirely on Agreth herself and survivability. The latter is a better long term approach, so it is what I would focus on for you
As a result, a sample team would be:
- Tuhanarak - healing, debuff removal at the start of her turn, decrease speed, decrease attack
- Reliquary Tender - Full cleanse and healing. I still use her in my Agreth team which works on hard doom tower
- UDK - Healing, shield. Turn off his A2 which is AoE, as you don't want to attack the spiderlings
- Old Hermit Jorrg - Revive, HP Burn and turn meter boost
- Djamarsa - decrease speed, healing, cooldown chance
Everyone in the above team would be built to sustain damage, such as HP (more than 30+), defense (around 2K) and speed (at least 180 odd). As long as none have an AoE enabled, then it is just a matter of time to take down Agreth.
If you find that you are surviving easily, then you can drop someone and bring in a pure damage dealer. No-one jumped out at me as being a good option in your list straight away though, which is why I focused on support champions
