City of Science
Note: I did not spend money on this game or promote spending money, you can spend money at your own will but just because it is in this solution I do not promote this game at all.
This one will take some time unless you are willing to spend money to obtain this achievement.
Using your library you can upgrade your units and Siege weapons. This will take a significant amount of time and gold because there isn't a ton of upgrades and for every upgrade the time increases to upgrade again.
Time is obvious, you are going to just have to do a ton of waiting, focus on upgrades that have the lowest times (will also be the lowest gold).
Gold is going to have to be earned to be the fastest otherwise it will take a while waiting for your buildings to give it to you. Since you will be upgrading your money making buildings make sure to log in all the time and collect them because they do have a limit they carry. If you want to earn gold fast you can work on the Campaign OR attack weak enemies. Also if you move up LEAGUES every league will give you a bonus gold from defeating opponents which means obtaining 1 star from a battle is a win.
I believe you will earn this at the Renaissance Age or Industrial Age (if someone can please confirm, this is impossible to have at the current time unless $$$ has been spent on the game).
How to earn a ton of free Jewels:
For those willing to spend money on this game:
To do multiple upgrades at the same time you can buy Libraries (which are what do upgrades) total needed is 3750 Jewels 1st is free, 2nd is 250, 3rd is 500, 4th is 1000, 5th is 2000.