Mt. Kolts consists of both indoor and outdoor areas, each of which features a different set of encounters. You'll go back and forth between these areas frequently, so be prepared for all of the enemies here. You'll tend to see a lot of side attacks in this area, so practice directing your physical attacks against the backs of enemies to dish out more damage.
Encounters: Caverns
All of the caverns in Mt. Kolts feature the same pair of possible encounters: 2 Brawlers and 2 Tuskers. These encounters require very different tactics. Brawlers are Berserk and will simply attack. They have higher than average defense, but low HP. Aside from absorbing damage from the Bio Blaster, they have no relevant strengths or weaknesses, so just hit them with whatever you have. It's possible to steal a Bandana, a nice upgrade for several characters, though it's rare. Tuskers, on the other hand, are beefy targets that have a powerful attack and an even more powerful counterattack. Fortunately they will only counterattack the Fight command, so stick to abilities like Fire (which they are weak against), the AutoCrossbow, and Steal as much as you can.
Encounters: West Face
The exact encounters on the slopes of Mt. Kolts vary, but in the first large area you'll most frequently be attacked by 3 Cirpii. Sometimes a Tusker will be added to the mix. The Cirpii are your top priority because on their third turn they may use Beak, which inflicts Petrify. Unless you bought Jewel Rings in South Figaro, this could be a problem. You should have a Soft or two in your inventory even if you haven't bought any, but eventually this could catch up with you. The AutoCrossbow will help thin them out quickly.
Navigating the West Face
The first section of Mt. Kolts will have you weaving in and out of caverns on the west side of the mountain range. You'll see a shadow the first time you go outside, and a few times on the slopes thereafter. The Central Cavern is where things start to get a little complicated. The path onward is found to the northwest, but you'll find very nice treasures if you follow semi-hidden paths to the east. The first is the more obvious of the two: walk south around the plateau in the middle of the cavern to reach the path to the Guardian, a nice upgrade for Locke. This gives him a nice boost to Speed, but more importantly it's a huge upgrade in Bat.Pwr which will make him your best physical attacker. (This is also good since he's the only current party member who needs to attack with a weapon to deal damage.)
Back in the Central Cavern, you may notice a path to the northeast, but no way to reach it. Simply follow the wall, going up or down whenever you can't continue right with your party out of view. This path leads to an Atlas Armlet, a decent relic that affects normal Fight damage. That makes it a good fit for Locke for the moment.
When you're ready to proceed, head northwest in the Central Cavern. You may notice that you're taking a lot of damage or using up a lot of Terra's MP here—this is the first dungeon of any real length, so be prepared to leave and regroup if you need to. You can use Sleeping Bags or a Tent or return to South Figaro or Duncan's Cabin to recuperate. The next time through, you'll likely have gained a level and won't need to explore as much, so you can make your way through the mountain further and further. Alternately, you can stock up on Tonics and Potions and power through everything. It's up to you!
The Upper Slopes
You will emerge near the top of this mountain and see another shadow. Follow it around to the other side. A new foe, the Trilium, appears here. This is why you may have wanted to buy Star Pendants in South Figaro: these guys inflict Poison with their Bane Touch attack. They often open combat with it. It doesn't deal any damage directly, but if you don't heal the Poison quickly it can become a problem. These guys are vulnerable to Fire like the Tuskers they sometimes appear with. If you have Poison protection, it may be best to save your MP, because Triliums are not particularly dangerous in terms of physical damage.
There are two entrances in this area. The first leads to a Tent which may be useful in the near future, while the second leads to the Bridge Cavern (so-called because it features a lot of bridges). There is nothing special here and only a single path which can be followed back to the mountain face where you'll find a much larger bridge connecting to another mountain face. Take advantage of the save point here, because you have an encounter-filled area followed by a boss fight coming up.
Once you deal 720 damage to him (his effective actual HP), he'll blow your party away with an attack, only to have Sabin show up. Once that happens, he'll hit Sabin with Doom Fist and you'll have until that countdown completes to use the Pummel Blitz. Once you do, though, the fight ends immediately, regardless of Vargas's remaining HP.
The East Face
Most of this area is laid out in a counter-clockwise spiral, with you starting at the outside and working your way in. You'll run into a lot of Triliums here, so be prepared to deal with Poison one way or another. The shadow you've been following is finally visible in this area, and it turns out to be Duncan's son Vargas. When you talk to him, he will attack, accompanied by two Ipoohs. You'll need to defeat both of them before you can target Vargas. The AutoCrossbow and Fire spell are effective if you want to hit both at once. They each have a Potion to steal. Vargas will use normal attacks and the relatively weak Gale Cut during this time.
Once Vargas is targetable, you can exploit his general weakness to magic as well as his specific weakness to Poison (the element—unfortunately he's immune to the status ailment). Locke can try to steal a Mithril Claw, though he's likely to end up with a Tonic. Your goal here is to inflict 720 damage on Vargas, at which point the battle enters phase 3.
When you've dealt enough damage to Vargas, Sabin will suddenly show up. Vargas uses his "Blizzard Fist" attack to blow away the rest of the party, leaving only Sabin. He'll quickly use Doom Fist on Sabin to inflict the Condemned status. Vargas has far too much HP to go through in that time, though he'll likely defeat Sabin with normal attacks before the timer runs out anyway. Once some time goes by, the game will give you the hint that need: a single use of Pummel (, , ) will end the fight immediately. Note that other Blitzes will work as attacks, but will not cause the fight to end.
Leaving Mt. Kolts
The entire party, including Sabin, will likely need healing after the fight is over. Give Sabin any equipment upgrades you have available and continue on: the exit is not far. Take a moment to see which Blitzes Sabin has available. He most likely has access to AuraBolt and probably Suplex as well.
There is a Tent in the next cavern after Vargas, and the exit is just past there. Oddly, the small area where you find the exit has a new set of encounters, including Vaporites you last saw in Narshe. They can basically be ignored at this point.
There is a completely optional cutscene available in South Figaro at this point. Sabin can speak to Duncan's wife about his apparent passing at the hands of Vargas. You don't materially gain anything by going out of the way to see this scene, but it's a nice tidbit.