You gain Au doing various things in the game. Completing missions and sub-quests in missions is the most direct way. You can also sell spare parts to net some change here and there as well.
Let's remember that taking lots of damage in a mission/breaking down/using a ton of ammo will cost you a ton in replacement parts and can be a real detriment to your money grind.
My suggestion is to play through the Order missions. You don't even have to get all the way through them to have tons of money, but it all does depend on your performance.
This will also put you on track towards several other achievements:
The Emblem Master achievement in Armored Core V worth 211 pointsGet all emblems and emblem pieces by buying them at the shop and/or destroying ACs.
The missions that involve you fighting a high profile enemy AC tend you net you more Au while (normally) reducing the amount of damage you take and ammo you use.
You could find a mission you are good and and can beat quickly without taking much damage/using much ammo and play that over and over again until you hit your 10 million.
It shouldn't take you too long to achieve this goal while also giving you a start on plenty of other achievements.