After the Returners' Hideout is threatened, you need to take Banon to safety on a raft on the Lete River/Lethe River.
River
24. Exocite
25. Pterodon/Lesser Lopros
On the river, take a left whenever you're asked. During battles, have Banon use Health/Pray at every turn.
During your journey, you will stop at a couple of save points. Feel free to use a Tent there and save the game. Then go back onto the raft.
Ultros
If you equipped Terra with the Genji Glove, equip her with a Buckler for this battle (go into her Items menu and press Up to change her weapons). Don't let Banon attack. Have him use Health/Pray only when you really need it. Terra should use Fire, Sabin should use Pummel/Clobber, and Edgar should use AutoCrossbow. If anyone dies, have anyone but Banon use the Fenix Down/Phoenix Down, then have Banon use Health/Pray right away.
After the battle, the group gets separated. After the cutscene, you will be in control of a Moogle, and you can save the game at a save point in the center. Then you can walk over to Locke, Sabin, or Terra/Banon/Edgar to continue their scenario. The three scenarios can be done in any order, and after completing a scenario, you will come back to this screen where you can choose another scenario, until you have done all three. Read how to complete Terra's scenario, Locke's scenario, and Sabin's scenario.