Fly to Vector and enter the Magitek Research Facility.
Walkthrough
In Vector, find the supporter who creates a distraction near the crates and enter the factory by the route behind the guards. Follow the pipes and conveyors, searching side passages before taking one-way drops. The disposal area leads to Ifrit and Shiva.
After that encounter, collect their magicite and continue through the facility. Climb through the research rooms, defeat 
Number 024 and stop the apparatus to receive more magicite. Take time to equip and heal before speaking to Cid and leaving.
The mine-cart escape includes a series of fights and 
Number 128. After the party reaches the airship, the Cranes attack. Concentrate damage while maintaining healing, then return to Narshe after the story scenes. Factory encounters and some treasure opportunities are time-limited.
Checkpoint
There is a save and recovery room west of the Ifrit and Shiva encounter. Pick up both pieces of magicite after the fight. Above the stairs, check the research room for a concealed chest before Number 024. After the elevator sequence, save and heal in the room beside Cid before starting the mine-cart escape.