The Serpent Trench
You don't have to go to Mobliz now, but you can earn the Fenrir Esper if you do. The plot progression also makes a bit more sense, if that's the sort of thing you care about. On the other hand, if you haven't recruited Sabin, the upcoming boss battle may be a bit too difficult. Regardless of your next destination, you'll want to head to the isthmus east of Tzen and northeast of Albrook. The Monsters awaiting you on the other side of the bridge are all new. (That is, of course, unless you rented a chocobo.
Any desert encounters will be with a Black Drgn, so make sure Celes and Sabin (if you brought him) have Zombie protection. Having either one turn into a Zombie isn't a game over, but there's a good chance they'll kill their ally. Ribbons and Amulets, the latter of which are available for purchase in Tzen, are recommended.
The one Monster you'll see on every other type of terrain is the Buffalax. They are relatively tough with 2,252 HP, but they don't have a deep bag of tricks. Their fifth attack will take the form of a three-hit combo ending in the ×1.5 damage Riot, and they will counter Magic by healing their group with Sun Bath. for 300–400 HP each. They are vulnerable to Fire, though they may heal their allies even as a counterattack to a Fire 2 Spell that finishes them off.
Wasteland areas also feature Delta Bugs, either in fours or in a pair alongside a Buffalax. They are highly resistant to physical damage, but vulnerable to Fire like Buffalaxes. In mixed groups, Fire Dance will dish out a lot of damage without prompting a Sun Bath. Delta Bugs can use Mega Volt, but lack the Mag.Pwr to make it truly dangerous.
The plains and forests share the same encounters. Aside from a lone Buffalax, you will often see a pair of Bloompires, sometimes alongside a Lizard. Like Black Drgns, Bloompires can inflict Zombie, and they'll also cast Bio for several hundred damage. They have near-impenetrable Defense and Mag.Def, but only 12 HP so they go down in a few hits at most. Alternately, use Cure (since they are undead) or an attack like the Atma Weapon or Pummel that ignores Defense. Lizards have no noteworthy defenses, and have a weakness to Ice, but can turn your Characters into Imps with Imp Glare. Assuming you're already protected against Zombie, they should be your primary target.
The good news is, you don't need to defeat Phunbaba in this battle. Once you deal at least 7,520 damage, he will flee. The most effective Spell to use is Bio, to exploit his Poison weakness.
Mobliz
Once you reach the Serpent Trench proper, head east and follow the land north to reach Mobliz The town has been destroyed, and no adults survive. You're accosted by dogs as you enter, but if you follow the child into the Post Office, you'll learn that Terra is here protecting everyone. She refuses to rejoin the party, though. After you leave, Phunbaba will attack, and you'll control Terra alone in this battle. You are meant to lose, so don't worry about how it goes (and don't waste Items or bother with Morph).
When Terra is defeated, your normal party will step in. This is a real fight that you'll need to win, though you don't need to take out all of Phunbaba's 28,000 HP. He'll flee the battle after taking at least 7,520. Bio will go a long way toward making that happen. He's also fun to Suplex, just because he's so big. Offense won't be your major problem here, though, because Phunbaba hits very hard.
Phunbaba starts off with a physical attack, potentially the triple-damage Solar Plex. He'll follow that up with Bolt 2 or Bolt 3. His third attack can be Bolt 2, Solar Plex, or Blow Fish. Blow Fish is the one you don't want to see, as 1,000 irresistible damage is going to be a problem in a small party. You could do this fight later with some reinforcements to make things a bit easier.
You'll need to decide whether to go all-out or fight cautiously. If any Character has beefed-up Mag.Pwr and has learned it, casting Bio can end the fight quickly before Phunbaba ever gets a chance to use Blow Fish. Otherwise, you may want to protect yourself with Runic and let Sabin dish out the damage. Just make sure to avoid Thunder, which Phunbaba absorbs.
Once you've won the battle, Terra still will not join, but one of the children gives you the Fenrir Esper. This Esper is an alternate source of Warp and Stop and teaches the new X-Zone Spell. There is a Fenix Down to collect in the top barrel next to the Injured Lad's House that wasn't present in the World of Balance.
You'll have to follow the Serpent Trench all the way back to where you started and continue north to reach Nikeah. If you want to avoid battles, take advantage of the Chocobo Stable in the western part of the forest south of Mobliz.