Skull coins are large coin figures that appear three times per level. They contain twenty lums that are collected when the coin is acquired. To earn this specific achievement, you must obtain a total of 216 of these Skull coins across all of your playthroughs. In order for the coins to register toward the overall count for this achievement, you must finish the level after collecting the coin(s).
A quick way to repetitively boost Skull coins is repeatedly finishing the ninth level, titled "Flying Fish Tails". The level takes roughly thirty seconds to complete per run, resulting in three Skull coins per attempt (unless you die). From zero coins it will take 72 attempts to net this achievement. 72*30 = 2160 seconds = roughly 36 minutes to complete this from scratch.
[this level is also great for boosting 20000 Lums if you don't want to purchase a pack of 20000 Lums for $1.99!]