Astral Gems are the Shadow Lords currency, those blue diamonds you use to buy packs.
This achievement isn't collective, so you don't have to collect 10,000 at one time.
You earn these naturally in the game, but playing story-related missions (ones with multiple quests), defeating Gargos, unlocking tank & skeleton chests, and fighting (instead of deploying) will all earn you extra. Should come around your second or third playthrough