I played around with the armchair GM tool on Cap Friendly and it's not easy for the Bruins to acquire Chychrun from a salary standpoint. It will probably require a 3rd team or retention. To make the cap work, without trading someone unexpected like Grzelyck or Carlo, they would need to move both Smith and Reilly.
Just from a salary standpoint (I realize there will be more in futures and picks), I put in a trade of Zboril, Lauko, Lysell, Reilly for Chychrun and then LTIR'd Lettieri and waived/demoted Smith and was still over hte cap by about $400,000. Smith would probably have to go as well, either in the deal or elsewhere. Our have Arizona retain or launder through a 3rd party. There's also the added complexity of the actual money (Zboril, Reilly and Smith are more expensive in actual cash than their cap hit) and the contract limits (Arizona goes +3 in this scenario bringing them to 47/50) and it's far more complex than it appears on the surface.