Before even beginning your farming adventures in Attack On Titan 2 I very highly recommend acquiring the skill 'Elimination Bounty' in Territory Recovery Mode. Basically just add Kitz to your team in Territory Recovery and go on some missions until he's level 5 bonded with you, this is when you will get the skill.

From now on, once the skill is equipped, during any mission you play get at least 10 complete eliminations on titans and then finish the mission and the amount of materials you get will go up an incredible amount, you'll easily get 20+ of each material that the mission gives you, especially when combined with the 'Form Material Recovery Squad' policy.

- Very Important -
The Elimination Bounty skill is especially important when farming for golden drops (more information about drop farming lower in the guide).

:IMPORTANT NOTE:
Valve keeps blocking any new links I post to the google sheet containing all the farming data. To solve this issue please copy the link into your browser manually instead of clicking it directly. Sorry for the inconvenience.

https://docs.google.com/spreadsheets/d/1a1_x94e3Jg-edkTyJ_fKVkdaUDxVOO_C2aCVRYZgFqA/edit?usp=sharing

This Is An Example Of What Some Of The Spreadsheet Looks Like:

To use the spreadsheet just follow the link and use 'ctrl+F' to begin searching for the item you wish to farm. Once searched, the document will highlight all the missions that give that item as a completion reward, these are the missions you want to play to farm for that item!

(Ctrl+F Will Bring Up A Box Like This That You Search For The Item In):

If multiple missions give the item you need I highly recommend trying out each mission and seeing what works best for you. Some missions give more of an item than others do, and some missions are much faster to complete than others. So experiment a little and find which one of the quests gives the most of the item you're looking for!

Rainbow Drops:
In short, rainbow drops are given for capturing titans in the game (albeit you need to capture quite a few). You can capture titans using character abilities (like Hange's), or you can use the capture net item yourself. There is also a skill that can help you capture large titans much more easily called Titan Hunter, which allows you to net titans after only one limb is destroyed.

The most guaranteed way to farm rainbow drops however, as you need to capture quite a few titans on a mission to get any, is on the scout mission (Another Mode mission) 'A Cornered Rat'. Set the difficulty to heaven (to give you infinite of all the items you're carrying) and start the mission, then use your infinite capture nets to capture all the small titans on the mission. Once you've done you should have 20+ rainbow drops (as long as you've used the Elimination Bounty skill, and Material Recovery Squad policy)

Scarlet Drops & Golden Drops:
By far the easiest way to farm both scarlet and golden drops at once is playing through Territory Recovery Mode on Eden difficulty.

Unfortunately golden drops can only be earned in Eden difficult once, and thats it. Even if you reset territory recovery mode progress, you will still no longer get golden drops. Scarlet drops will always be available however. Because of this, if you have yet to play through territory recovery on Eden, wait until you have Kitz's skill (Elimination Bounty), and play through each territory recovery mission on Eden using this skill, which should get you about 20+ scarlet drops and 20+ golden drops each territory mission. Again though, this only works on a first time playthrough.

If you have missed this prime opportunity however (like I did for quite a few of the Eden missions), golden drops can still luckily be obtained through the wings of freedom exchange for 100 wings each. Scarlet and rainbow drops can also be bought here if you need to, but of course these should really be very easily farmed.

I hope this guide and spreadsheet will be very useful to you all! Currently it is a work in progress but its being updated very often and will be completed soon. If you notice any mistakes in either the quest rewards or spelling errors, please leave a comment on the Steam guide and I'll get it fixed as soon as possible.