To get this achievement you'll need to use one of the new crafting tables called Compost Bin to compost 10,000 materials. You make the Compost Bin by using the old gardening bench that is now called Antiquated Gardening Bench.
When you've got access to the Compost Bin you can compost old materials you have in your inventory. The best material to compost would be, eye of Q'bthulhu. These are easy to get by loot grinding shadow rarity gear or by farming Shadow Towers for shadow caches. They can also be bought from the in game marketplace but prices on materials that can be composted have increased with this updated.
You can compost all of your battle tropies aswell to help free up your build inventory space which you'll need for the new plants for the other achievements this update has.
Hope this helps.