What rank are you? This will dictate where you grind.
In Spiral Knights, you should generally try to grind the places with the most crowns or rarities. That way if you are unlucky and don't receive Orbs of Alchemy from these levels, you still should have enough crowns to buy some.
For example if you grind at Royal Jelly Palace, you have the chance to find 3* and 4* orbs. If you're not lucky with the loot boxes, you will have enough crowns at that point to buy some.
You will really want to grind boss levels that give lots of crowns as well as have a lot of prize boxes. The best in T2 is Jelly King and best in T3 is Vanaduke.
TLDR; Grind levels that give lots of crowns and just buy orbs yourself. If you are lucky the levels should give orbs.
This strategy will be staple throughout most of the game.