Bump...

Well bud, you're biting off more than you can chew. You only have 5 level 60's and 2 of them are rares. While Alice is decent for Spider, the rest of your team isn't.

Of the champs that you have, Stag Knight or Michinaki should be your next 60. Unfortunately, neither of them are great for spider with perhaps Mich being the better of the two. However, Stag Knight is an excellent all around great champ and would say he's S tier. He is a serious work horse for an early to late game account.

Stage 13 is what you have to settle for now. Until you get better champs, that's all you can do for now.

I would give a very strong nod to Scyl as your next L60.  She is an incredible support and will help you advance in all dungeons, not just spider.  After Scyl, I would absolutely go with Stag Knight, and then probably Skullcrusher.  

Stag Knight will help you everywhere, and Skullcrusher is a beast for Clan Boss progession.  There are only 3 full team Counterattack toons in the game.  Count yourself lucky to have pulled him this early.

As far as Spider progression goes, one of the most effective strategies for climbing Spider is Stun/Burn.  Scyl is a decent Stun toon and you can make her better with a set of Stun Gear.  

Skarg is an amazing Burner, and you already have him at L60.  As long as you have three debuffs on the target, his A2 will put HPB on all the spiderlings, whcih will melt the boss.  His A3 also gives unresitable fear on the spiderlings, which will supplement the Stuns from Scyl.     

Of the toons in your screenshot, the best options to get debuffs out there are probably Stag Knight & Alure.  You want Scyl & your debuffer fatster than Skarg.  You can expect Scyl to land a few Stuns, and then you'd want Stag Knight or Alure to use their A2, which will give you three debuffs on a few of the lings. Then drop Skargs A2 on one of the spiderligns with 3 debuffs and take the win.  You can climb all the way to L25 with good gear on those toons.