Yes,  you  need  to  kill  that  level  of  clan  boss  to  get  your  second  chest.

thanks,, I had assumed that, but to remove all doubt

Youll also want to check the damage output required for max chest nm is 39 something mill and unm is 70 something mil so make sure to do that amount of damage to get those rewards. im only saying these two cause i dont remember the other difficultys off the top off my head but yeah def check. thats where the terms 2 key or 1 key teams come from i run a 2 key unm team meaning in 2 keys i can get the max rewards my friend Harley Quinn on the other hand is a whale and she can 1 key unm she does 70+ mil in 1 key. i know you didnt ask all of this but just throwing this info out there so others can learn as well.