Barret recommends the party split up. Once the player controls Cloud, simply walk over to Tifa, as the ID check begins. After this, Tifa requests Cloud check the next car for Barret. Walk over to him in the next cart to see a cutscene involving him. Pick up the Healing Materia on the seat on the left, and then return to the cart to check on Tifa. An ID scan will begin. Approach Tifa, and a cutscene will commence, at which point several Slug-Rays will appear and a three-minute timer starts for a lockdown. The Slug-Rays can be dealt with using Cloud's Braver to destroy several when clustered together, or simply with a magic attack (they are weak to Lightning, meaning Thunder is a great spell against them).
Once defeated, Tifa and Barret will leave to the next car; destroy a few more Slug-Rays (more durable than the last) and head further north for another cutscene. After this, Tifa joins the party, and more Slug-Rays are fought. Cloud can use the same tactics, while Tifa can use her martial techniques. Once defeated, the two hear a voice from Barret, and must run over to him. Follow the tunnel north, as a quick cutscene commences. Continue forward, and Slug-Rays are fought alongside security officers, against which the same strategies apply. Continue north and the party will find Barret, who encourages them to use the stairs to reach him. Take the stairs on the right and use the walkway to regroup with Barret.
Barret joins the party, as more Slug-Rays are fought, along with security officers and grenadiers. Barret can use his Overcharge to pressure the Slug-Rays, and magic spells to defeat the enemies when clustered together. Once defeated, a cutscene commences, leading into the next quest, "Find Stamp".
Hard mode tips
Though the enemies are more durable than before, the tactics are similar. Slug-Rays can be dealt with using Cloud's Triple Slash and Tifa's character abilities, and their main threat is Luminous Blast, which can stun a character. The Slug-Rays should be attacked before they can use this ability to interrupt it.