Chopperman Missions

Chopperman Missions or more officially Requests from Chopperman is a new feature added in version 7.0 (August 2).

There are three types: Weekly, Rookie and Special. You complete them automatically upon doing whatever they requested; they are not retroactive (ex. for a Rookie mission to clear Alvida's Hideout, if you have cleared it before the mission was announced you will have to clear it again to get the Chopperman reward).

Weekly are the same every week, they repeat and can be easily completed. If not completed they expire and reset at the end of the week.

Rookie are unique, they can be completed at your leisure, but cannot be attempted again.

Special are unique, usually tied to some weekly event (like Neo Clashes), will expire at the end of the event and will not come back.

Weekly
We may list them here (please do), but anyone can look them up in the game at any point...

Rookie
Rookie missions, list courtesy of reddit user M1STERBUTTONS

There are 80 in total, but 15 of them gives you super easy Chopperman events at Extra Isle, each of which gives you increasing amount of EXP:

Quest No. 4 - 175 XP

Quest No. 11 - 750 XP

Quest No. 17 - 4.000 XP

Quest No. 27 - 8.000 XP

Quest No. 33 - 12.000 XP

Quest No. 37 - 50.000 XP

Quest No. 40 - 25.000 XP

Quest No. 45 - 25.000 XP

Quest No. 50 - 50.000 XP

Quest No. 56 - 50.000 XP

Quest No. 61 - 50.000 XP

Quest No. 66 - 50.000 XP

Quest No. 71 - 100.000 XP

Quest No. 77 - 200.000 XP

Quest No. 79 - 300.000 XP

Keep in mind that you can only store 2x your stamina, so you may want to be careful when you complete them to avoid wasting stamina by leveling up multiple times. Further, keep in mind there are units that boost EXP (Neptune King of the Ryugu Kingdom with 50% boost and Trafalgar Law Straw Hat-Heart Pirate Alliance with 20% boost) and there are two ships (not yet on Global), the 3rd Anniversary Thousand Sunny with 300% boost (expect it around February 2018) and the Bazaar's Flying Dutchman with 50% that also help. Out of those, the 3rd Anni is the best, so it is recommended to wait for it before completing the missions. Using those units the total amount of EXP you can get is as follows (table courtesy of reddit user ReadAccount):

Special
We had so far special missions during Neo Raids (Doffy and Aokiji). They had good payouts (Forbidden Tomes, Universal Skillbooks) but also require clearing the relatively difficult events up to 90 times (to clear 100% missions).