Is it possible to earn enough skulls to unlock everything in Orcs Must Die 2?

Solution 1:

Yes.

Due to the fact that bonus skulls can be achieved over and over again (unlike the skulls for completing a level, which are only achieved the first time you get that amount of skulls), you can theoretically receive more skulls than you need to unlock everything.

This means that if you've 4 skulled a level, and then you 5 skull it and also get 5 bonus skulls, you'll receive 6 skulls. If you then complete the level again and again you 5 skull it with 5 bonus skulls, you'll now receive 5 skulls which are the 5 bonus skulls which you will always be able to receive.

Solution 2:

I believe there is another scoring system besides the story mode, lets say in endless mode the stats shown below there are bonus skulls to be earned for every increment 1000 career kills and there are bonus skulls to be picked up and skulls for every 5 waves you survived.

I played endless mode a few times and it does gives you lotsa skulls (bonus skulls) either than the ones awarded for every stage (the 5 skull limit)