Another recommendation is to treat spiders like you deal with Chrysallids in early game: Don't.
Whatever place they're attacking will probably do just fine.
That, or bend the rules a little by using Debug mode.
I remember my first spider attack + underground mission that happened in Japan (funnily enough). It was done before special spider types were implemented, and it still was quite a terror. Ironically enough, taking alive the queen was relatively easy, as IIRC it is hidden in a room it cannot leave, making it easy to shoot her down.
However,
The worse is still to come. You won't see the last of these bloody insects anytime soon.
LP back at the Codex when, Slaugh? ;)