In Bowser’s Fury, each of the islands has a set of Bowser Fury blocks — silver blocks with Bowser’s logo embossed in black.
These blocks can only be broken by Fury Bowser’s fiery breath, so you’ll need to wait for Fury Bowser to appear before you can access the Cat Shines behind them.
To break them, simply find and stand near the cluster of blocks while Fury Bowser is rampaging. He’ll send out several stone pillars that land near the blocks, so you can safely stand behind those while he blasts the blocks away.
After the blocks are gone, a Cat Shine will be revealed behind or under the blocks. Grabbing the Cat Shine will damage Fury Bowser, and he’ll immediately leave. If you want him to stick around and blast more blocks, don’t grab the Cat Shine. The blocks will stay broken forever, so you won’t have to worry about them respawning.
Each island has five Cat Shines, including those behind Bowser Fury blocks. You won’t need to break all of the blocks to beat the game.