BALAN WONDERWORLD

Before going for this achievement, it is HIGHLY recommended that you get the reward for doing the Tim of Legend achievement, as it will help tremendously with getting around the stages faster and without taking damage.

To find this enemy, you need to be in Hard Mode. You enter Hard Mode by killing a bunch of enemies without taking any damage (from any source) - the best place to do this I think is 6-2. Run in circles killing enemies (Pumpkin Puncher is a good costume for this) until enemies start appearing red. These red enemies mean you are now in Hard Mode, and when you finish the level you will receive a red stamp instead of a gold one.

Once in Hard Mode, the Lanced Multipli will appear as the mini-boss in either 2-2 or 4-2. If you have already spawned or defeated the mini-bosses in those chapters before entering Hard Mode, you will have to defeat that chapter's main boss to reset the levels. When spawning, the mini-boss will either be red or purple - you want the purple one. If the red one spawns, IMMEDIATELY quit to console, DO NOT return to the Isle of Tims or you will have to reset the level again by beating the chapter's main boss. Quitting to console will allow you to keep trying.

I don't know how rare the spawn is - I got a LOT of red enemies before the Lanced versions showed up (except for Multipli). I think killing regular enemies in the level helps but this is pure speculation and hasn't been confirmed.

As a final tip, if you get hit during the Lanced fight and you still have other Lanced enemies to fight, finish the fight, then when the achievement pops you can quit to console and keep your Hard Mode status. Good luck!