Is this an example of chaining adjectives?
The sentence should be understood as such: 
[没来得及避开的] 很快 就[被骷髅们] 蜂拥而上，撕成碎片

没来得及避开的: the ones that don't have enough time to evade. 

很快 is an adverb soon, quickly. 

就 denotes something happens very soon. 

I tweaked your understanding: 


  those who didn't have enough time to evade were soon/quickly swarmed by skeletons in excess and torn into pieces.