Let's say a skulltula has a requirement like "Do not take more than 4 hearts of damage". If I'm playing co-op, does that mean we each can't take more than 4 hears, or we can't take more than 4 hearts total? What about other numeric requirements?
The requirements are shared for both players.
That means that if you need to kill X number of enemies, it considers the kills from both players, and both players cannot lose more than X number of hearts between them. If a challenge specifies that a player must maintain above X% of their health (I believes there's 2 of these), that threshold must be maintained by both players.
Playing co-op can be both a curse and a blessing in this regard! Though I found it very useful to have a partner when tackling bosses with a time limit.