300 points are required.
The three highest rewarding support quests add up to 70 points (Please Find My Cat [30 points], Please Find My Cat 2 [10 points], Kappture the Kappa [30 points]). They're all available from the start of Part-Time Hero, though Please Find My Cat has to be activated and two of the kappa statues are locked until reaching chapters 6 and 7.
Alternately, the Missing and Shit Out Of Luck tasks award 43 and 15 points in total, with Missing just requiring tracking down 5 people and Shit Out Of Luck requiring delivering 21 packets of tissues, which costs 4200 eco-points.
There's also 24 SOS quests that award 97 points, but requires chapter 15 to unlock them all. They involve defeating a small group of enemies at predetermined locations.
Food delivery quests can net 65 points, but requires access to Sotenbori. All items and where to find them can be found on the walkthrough
Yakuza: Like a Dragon WalkthroughMiscellaneous item delivery quests award 51 points, but requires access to Sotenbori. There's also a bit of RNG with getting the eggs from Omelette (though saving before Omelette lays the egg can help with savescumming).
Finally, takedown quests, which require taking down certain enemies encountered in the field, award 160 points in total, but can be really finicky depending on spawns, especially after all the enemies get upgraded, or require trailing through dungeons to find guaranteed spawns. It may also require reaching the late game for certain quests to activate.
Altogether these tasks should award about 500 points in total, giving a lot of wiggle room for mixing up the tasks. I've left off prize delivery quests because the crane game is too frustrating and the early bug quests are too RNG-heavy/reliant on Can Quest to aim for