The Kirby, Waddle Dee, and Meta Knight masks will permanently unlock once you go to the level select screen while you have StreetPass for Kirby: Triple Deluxe turned on.

Unlockable	How to unlock
Dedede's Metal Mask	Complete all Normal Stages.
Kirby, Waddle Dee and Meta Knight Masks	Load the game up while having Kirby: Triple Deluxe's StreetPass data installed on your 3DS.
Normal Extra Stage	Complete Normal Stages 2-6 with any rank.
Normal Stages 2-6	Complete Normal Stage 1 with any rank.
Special Extra Stage	Complete all Normal Stages and Special Stages 1-6 with a Gold or Platinum rank.
Special Stage 1	Achieve the Gold Trophy total score for Normal Mode.
Special Stages 2-6	Complete Special Stage 1 with any rank.
Taranza Mask	Complete all Special Stages.