It's a good thing you can't farm stage 15 - because you shouldn't :)

Spider has a bit of an odd difficulty curve - the strategies that work on the lower stages - such as the one you're using with your team, IE, clearing the spiderlings, are actually counterproductive on the higher stages, because they just have too much HP.

Rather, the strategy on the higher stages is to tank/CC the spiderlings, and use TM control to prevent the boss from getting a turn.

Drex works well, as long as the boss green affinity, since that'll ensure he's targeted. But he's completely useless against other affinities - he just has no reliable way to ensure he's being targeted.

UDK is your best friend here. He doesn't care about affinity - he'll *always* be targeted. So, you put him in high-resist gear, and make him tanky, and then you only need to worry about the boss.

For TM control, you have Coldheart and Armiger. Those two should be able to do the job on their own.

To round out the team, you just need people who can keep UDK alive. Duchess is very good at that job. To round the team out, I'd add Apothecary, just for extra healing and speed up for your team. If you find you don't really need the healing, then you can use Visix instead, for extra TM control.

If you can't nuke it, use Mordecai. :)

To add to what kramaswamy.kr said, if you have a decent set of stone skin for UDK it helps as well. If you have decent turn meter control you don't even need to worry about his stats. The slower you can build him the better. 

Note that if you choose to use UDK as your Spiderling Tank, Drexthar is useless as he won't be getting hit. If you want to go for a HP Burn build (which you should at lower account levels) I'd go with Mordecai as Fathertron suggested.

I run my UDK in 6-piece Stone Skin @ 116 speed. Everyone else on my Spider team is 2+ times faster than UDK. The spider is normally dead before UDK's Stone Skin buff has even expired.

Where do you see Mordecai in the Screenshot he posted?

To reach stage 20, a team of UDK, Armiger, Coldheart, Scyl, Stag Knight should work. In magic affinity stages, swap Armiger for Visix. You have to do each stage up to 20 only once, it's not worth farming below stage 20.

In stage 20, wich is spirit affinity, take UDK out and use Drexthar instead. That will speed up the fight a lot. If Drex dies, Scyl can revive him with ally protection, but with decrease atk on all Spiderlings (Stag Knight!) and enough res to resist the poisons (~ 350), he shouldn't die at all. Lvl 60 of course, as he is the punching ball.