>>723937969
From a gameplay perspective, the key is that you can't pick up anything too much bigger than you, so you have to work your size up so you can pick up bigger shit.
As for the goals, it depends on the level:
>get above a certain size threshold within a time limit (bonus points for passing the required size)
>get above a certain size threshold within a time limit (also your katamari is fast as hell and you can't stop, it only goes forward and you can kinda control the speed)
>get as big as possible only picking up a certain type of item, and the level ends if you pick up [certain other item]
>with no guides, get your katamari as close to a specific given size based on an estimate you get at the beginning of the level
>collect X item as much as you want with no time limit, and they respawn, and you can quit whenever you want to add it to the tally (the final goal is comically huge)
>there are 1000 of [item] in the level, get as many as you can within the time limit
>there's a meteor heading for Earth; roll up the continents to get big enough to stop the meteor
>roll up hot things to stay on fire, if you roll into water or you pick up hot shit too slow, the fire goes out and you lose. Finish the level by rolling up the bonfire
>you have unlimited time to roll up the solar system and all the shit you put in it. If you roll up the sun and you're big enough to do it, you win
Most of the games also include a lot of collectables like cosmetics and characters, some are well-hidden, some are only available within a time frame, some have random unlock conditions like playing a certain character on a certain level, and some just stick out like a sore thumb to make it easy to get them.
TL;DR:
>>723938381