The Illusionists are merely three copies of Layazero, which could be explained by the holographic nature of Layazero itself, copying itself and creating two duplicates. The Illusionists do not have a mission, and upon defeat, the player is taken to the middle Meteo of the Multi mode of Star Trip and is given the neutral ending.
Put simply... what are you doing here? To go to the Illusionists is to intentionally fail. You can only reach here at your own hand (unless you're on a lower difficulty and are stuck with Yooj on Clean Air Club, though even that's questionable) and going to this group will always be bad for your score. Since you are (obviously) limited to using Layazero in this scenario, there will not be separate sections to denote a Layazero-specific strategy. As with Rare Cultures (or Hevendor Realm, for that matter), destroy the opposing Layazeros one at a time; target one, then the next, then the last. Due to Layazero's low scoring capability do not worry about earning points; you won't be earning that many anyway. If you are, just drag the battle out for as long as you can, though it will ultimately make little difference. Once you have finished this grouping, proceed to defeat Meteo, then sit in the corner and think about what you've done.
Molten Hellions | Chlorophylls
Stray Planet | Mechatropoloids | Earth Lovers
Bubblies | Dimensionals
Electric Nymphs | Hot & Chillies | Clean Air Club
Twin Moons | Illusionists | Rare Cultures
Meteo | Hevendor Realm