Zygarde would not go on the ship since she would see it as the territory of all the legendries and taking one step on it would have all the Pokémon gang up and most certainly beat her. She would see the MC as the source of the potential apocalypses but also could prevent a other apocalypses down the road so she would test him. The chase could start outside the ship at the harbor and go though shipping containers and cranes but it starts right outside the ship that the legends that could be on the ship to watch and be like a cheer squad since the other legends that could be caught always stay on the boat and his current legends would be released to protect the boat and populated areas without needing to mention what they do.
Another idea for the hatched Pokémon could be a image but they are in a chibi like baby form that would look adorable if it can be put in when they first hatch. Who does not love cute legendary babies looking adorable.
plus zygarde would be similar to Rayquaza for babysitting two legendaria's from fighting and now the MC has brought over an even bigger migraine that it will not allow. The persinality of zygarde does fit to what would be needed for a legendary to come out of the wild and be in a more potentially populated location This could show how much zygarde puts importance to the environment since it is the source of her power and would hold back. By having it in a Populated area she would not hold back if the threat is great enough. She could say when before she allows herself to be caught "I need to keep an eye on your situation so the apacalyps that your could make does not happen plus having some helpers/babies would reduce my workload for the future".
After the battle the town or city could hold a festival to thank the MC and the legendary pokemon that helped defend the city with a special festival (optional?) it would give the MC a (potion) to use that when the MC drinks it, it would allow him to have a massive orgy with his legends ALL AT ONCE. A description of the scene after the MC left the festival and retured to the temporary base (not the boat) could have "The air in the room was thick with lust and passion my every touch on their bodies would send waves of plessure to them as they quickly gave in to the lust in the atmosphere. One was riding my dick but the others could not wait their turn and did not care what part of me was in them as long as they had a part of me in them. One took my left hand, another my right in their dripping pussy. Yet another two took my left and right feet in to not be left out. That was not all another was under me rubbing her juices on my back while my face went to the biggest of the girls yet I could still breath fine. I was totally encapsulated everywhere in the flesh of love and I could feel my body reacting perfectly to each and every one of them like my dito genes had evolved even if temporary and I just had to sit back and enjoy the ride. Everyone could not tell when one began and ended but one thing was sure this would not stop till everyone was satisfied and the night was still young. (Morning) I woke up still in the same position, the center of all this, with each of their heads resting on my body with smiles and inflated bellies. Only one thought crossed my mind "I need to get the recipe for that potion"". This could then allow future parts on boat to have giant sex scene with many legends at once. Even if the player did not choose the festival a vilager could give a sample with the recipe to a worker on the boat that would then be sent to professor Maple to study and improve to still allow this choice in the future.
I did have an idea that could foreshadow one of the legendary of Gen 8 and would connect this to it well "A day of darkness is coming again and you may be able to prevent the destruction it will bring" I did read zygarde was at the first day of darkness so she saw the destruction there and could see the MC as a potential way to sLAY eternatus. I do have more ideas for this but don't want to go to far if this is to big or complex to be even included or see what Brpdchainsaw thinks first if they may be interested to hear more or not.
Thank you for hearing my idea!