The following buffs/debuffs helped me to beat the Nether Spider:
Skadi is right, except I'd recommend Sethallia over Serris for the buff stripping job, because Sethallia will also do a cleanse (though single target) and heal, plus a chance of HP burn with her A1 that will help take the spider down faster. And last but not least, Sethallia's buff strip is on a 3 turn CD if booked, 4 if not, while Serris' is on a 4 turn CD at best. Those 4 turns may be too long to immediately strip the spiderlings' buffs each time. Though if your Sethallia isn't booked, guess it's 4 turns either way.