Can players battle in the sky city?

The floating metropolis is the social hub. Shops, NPCs and the egg-hatching facilities are all there, which means the place you go to restock and hatch is also the place you fight other players. You are not travelling out to some separate arena to find opposition.

PvP is a standing part of the game rather than a one-off feature of the city, so expect player-versus-player modes to sit alongside whatever you do in the hub. If you want to learn a fight without another person on the other side, Holo-Battle Interlink can be challenged solo and fills your empty slots with AI teammates. That is the low-pressure way to work out how a team performs before you take it against someone who is trying to beat you.

The other place players fight each other

Operation: Egg Heist, also called PvP Egg Heist, Diamond Egg Heist or Diamond Egg Stealing, arrived in the third beta and is built around collecting exclusive Aniimo eggs. What it actually is has not settled. It has run as a competitive race between teams to collect eggs, as a PvP-only mode in teams of three, as a real-time PvEvP mode in the Lost Isles where three-player teams fight monsters and other players to gather and extract eggs and resources, as an objective-holding match between two teams, as a team-versus-team match with up to six three-player teams contesting a single objective, and as a cooperative mode with no PvP combat in it at all.

The common thread across those versions is three-player teams and eggs. Everything else about it is build-dependent, so treat the mode you get in one build as the current shape rather than the final one.

Not settled: Operation: Egg Heist has appeared both with and without PvP combat, so the amount of fighting other players you get outside the floating city is not fixed yet.