Bloody Palace is a survival mode that has been in every Devil May Cry game (minus the first one), and it is coming to Devil May Cry 5 as a free update very soon. The mode will be available on April 1. Here are some more details directly from the press release announcing the update.
“Bloody Palace is a survival mode that pits you against hordes of increasingly difficult enemies and bosses whilst racing against the ticking timer. Play as Dante, Nero or V in Bloody Palace Mode through multiple levels of enemies and truly test your SSStylish skills.”