Back to Sazh and Vanille, the quickest, and safest, route is to head left until you reach the 8x Segmented Carapace then take the second right to reach the next Sphere which holds a Phoenix Down . Some enemies are fairly strong for only two people so this route offers a good way to avoid the worst fights and reach the Thermadon guarding the waypoint quickly.
The Undermine Paradigm will come in very handy as you make your way round. After the cutscene, you should take out the Vespid Soldier before taking on the Thermadon. Once again, Undermine will provide a nice and easy way to defeat this pair of enemies, turning a difficult fight into a simple one.