To unlock this achievement u must obtain the following
Demolition Suit-Batman-Level 1-1-You Can Bank On Batman
Technology Suit-Robin-Level 1-1-You Can Bank On Batman
Magnet Suit-Robin-Level 1-2-An Icy Reception
Glide Suit-Batman-Level 1-2-An Icy Reception
Sonic Suit-Batman-Level 1-4-A Poisonous Appointment
Attract Suit-Robin-Level 1-4-A Poisonous Appointment
Heat Protection Suit-Batman-Level 1-4-A Poisonous Appointment
Water Suit-Robin-Level 2-3-Under The City
You will get this achievement during your hero playthrough and it cannot be missed.