Through initiating Style Action and whacking some enemies, you will be given access to the Crew Strike (given you've got a Crew Member attached to switch to). All you have to do now is to defeat a combined total of 10,000 enemies, across all stages and crew members, to obtain this trophy. You'll most likely end up getting this eventually throughout your playthrough with the game, as there are enough trophies in the end to keep you occupied for that platinum.
Note: This does not include any killed during Style Action or in regular form. This can only be obtained during Crew Strike (initiated with
after building the gauge in Style Action).