Normally there is only 1 item per big monster you kill for the battlefield quests...
Look through the other battlefield dungeons and see if there are any more monsters... they should drop the rest of the things. Its possible that that the spider dropped a couple of things... but most of them were not quest related, only the belt of surprise.
In act 1 there are 3 dungeons... each with 3 levels. (from act 2 onwards there are 6 dungeons). Every time you find a battlefield key, it should unlock another dungeon for you.
