All hunts that I’ve participated in have had a time limit of 30 minutes. Each island has gathering nodes (ore, mushrooms, flowers, etc.) and critters from which players can get general resources. There is no competition between party members for these resources, as everyone can gather them the same number of times. Since the mission automatically ends once the monster is defeated, most of the hunts I’ve been on started with everyone wandering around the island for a bit gathering resources, then once someone found the monster he or she sent up a flare and waited for at least the majority of the party to gather and fight it. The 30 minute time limit was always more than enough time for this pattern of activity. Each monster I fought felt a bit different from each other, with some of them having clearly defined combat stages. Sometimes monsters would even fly or burrow away and would have to be relocated to continue the fight.
Once the monster is defeated, the screen will automatically cut to a list of all the materials you personally gathered on the mission, then transition to a spotlight of the highest damage dealer for the fight, before then moving onto a new screen where players are awarded scores and trophies for their performance. Finally, loot caches will be distributed to players (one each), of varying rarities. I’m unclear whether the rarity of the cache has anything to do with the aforementioned scores/trophies or is completely random. These caches can be opened at special unlocking devices in the city and contain crafting materials.