Talk to the Prinny at the bottom of your secret base quickly and repeatedly. This can be done easily by holding Circle and rapidly tapping X until the confirmation message appears. When this happens the costumes shop and the Etna, Flonne, and Laharl costumes will become unlocked.
When you throw the indicated Darkdeath item into the spring that randomly appears inside the dungeon the corresponding Giga version of Darkdeath will be thrown back. The spring often appears at Mid-Tier Hero Mastery Cave and you can only use one spring for each piece of equipment. Note: There is a chance that the item will not be returned when you throw it into the spring.
Unlock G-Darkdeath Body: Throw Darkdeath Body into the spring.
Unlock G-Darkdeath Head: Throw Darkdeath Head into the spring.
Unlock G-Darkdeath Left Arm: Throw Darkdeath Left Arm into the spring.
Unlock G-Darkdeath Right Arm: Throw Darkdeath Right Arm into the spring.
Unlock G-Darkdeath Leg: Throw Darkdeath Leg into the spring.