What is the easiest way to get Antlion Mandibles in Terraria?
Solution 1:
Update: Terraria 1.3 brings with it seriously buffed antlion mandible drops, as well as a whole host of new kinds of antlions to drop them.
Getting enough for whatever you need should now be a lot easier, after running through the Underground Desert a bit.
Kill antlions.
While that answer seems facile, I'm afraid it's not just the easiest way, it's the only way*. And it takes approximately forever.
To speed up the process, you can engage in the construction of a mega project: Start a new world and convert it's entire surface to a desert, seriously increasing antlion spawning. The sand you need can be gathered from the antlions themselves as they start to spawn, as they are capable of producing an unlimited amount of sand. (Although getting any reasonable quantities of sand that way also takes, you guessed it, forever.
*: I say it's the only way, but in truth there is another: Find a server and trade for the mandibles with someone that has already done all of this.