After chasing the water monster into the mine, you'll watch it freeze a puddle and continue running away. once you catch up to it, it'll run one more time, and then begin spewing water. Catch it and start fighting.
Mini Boss Battles: Living Statues
These aren't too hard to beat, but there ends up being many in the mines. It's got a weakness to fire attacks, so try using Heat Wave on it for good damage. Ragnarok is another high damage dealing attack that works well here. The statue's favorite attack is Water Blessing, a group attack that deals water damage. Once it's defeated, it drops the Frost Jewel, an item which will let anyone use the Psynergy Frost. This is good for people experimenting with alternate Djinn builds as it saves them from having to disable all of Mia's Djinn every time they need to freeze something. Also, the water drains from the first level of the mines and the town, so a few new buildings will be accessible. Climb down the ladder, use Frost on the puddle left behind by the receding water, and jump out of the cave.
The first boss battle takes place in an area called "Altin Peak", but it's not the real cave entrance. Once you've defeated the Living Statue, go back to town and climb down the ladder near Sanctum, which no longer leads into water. Enter the Mine door with the railroad tracks leading into it. The potion shop is now available in Altin, so use it if you need to. You may want to bring antidotes (or simply use Mia's Cure Poison ability) because some monsters in the mine can poison.
In the newly opened mine entrance, follow the railroad tracks all the way to the next room, ignoring any side paths that you may see. Do the same in the next room, which will lead you to a large chamber filled with water. You can hear a Living Statue in here. Walk along the left wall to the north until you see a mine cart. Head to the right a little bit until you see an arrow pointing to the left in front of a switch. This controls the direction of the tracks; hitting the switch will change it to the right, allowing the cart to go on. Turn around and jump in the mine cart, which will lead you down the tracks and over a gap onto the island in the center where the Living Statue is. Fight this one in the same manner as before.
After that Statue is defeated, all the water will drain from the room. Take the mine cart back across and leave the room. Go all the way back to the first room and enter the door that you passed before. It was flooded before, but now the water is gone. Climb down the ladder and enter the next door. When you reach this chamber, another wide room, follow the tracks to the left until you see another switch. Flip it, and then turn around and go back to the right. Hop in the mine cart and ride it down the tracks. When it stops go through the door. In this room, go to the left until the path splits; the route continue left leads to a dead end with a Mimic, and the south path is the correct one. Go south through the next door. Before climbing the ladder in this room, walk to the left and freeze the puddle with Frost. Go back to the ladder, jump across the path you created, and enter the door.
This next room also contains a Living Statue. Climb down the ladder, walk to the left a little ways until you see a path heading north. Go up that path and freeze the puddle with Frost, so that you will be able to reach the mine cart. Once it is frozen, go back and climb the ladder on the cliff which served as the wall to the path. Jump across the ice pillar, get in the mine cart, and ride. When it stops, open the treasure chest and take the Dragon Shield. Take the mine cart back, then follow the same way you took to reach it, back down the ladder. Walk to the left until you see another ladder; climb it, walk north and hit the switch. Return to the mine cart. Get back in, and when it stops this time, walk right and climb down the ladder. Challenge yet another Living Statue. Once it is defeated, exit the dungeon temporarily, easiest by using Retreat.
At this time, all the water should be drained from the town. The armor and weapon shops are now available. check the Altin page for details on what to do in town now that it's all accessible.
To reenter the next problem area of the mine, climb down to the lowest point in the town, and go into the mine shaft. Save before starting the next section. Once inside, follow the railroad tracks to a split. Take the right path, still following the tracks, through two more doors. The tracks end in this room. Head south and open a treasure chest, then move out to the right. Keep going down this path and through the next door. This room is another large one with a mine cart. First, walk to the right until you see a stump. Use Move to slide it one space to the left, then Frost the puddle next to where it was. Climb the ladder to the north, flip the switch up there, then go south and jump across the path you just created. Jump in the mine cart. When it stops just get back in. This time, it will lead you to a Mercury Djinni. Fight it, and collect Spritz. Spritz is very useful as it heals everyone in the party. Get back in the mine cart one last time, and then go left, Frost one puddle, then walk left and Frost another. Go back towards the mine cart and climb up the ladder that is there. Walk down this path, jumping across the ice pillars, and upon reaching the other side enter the door.
In this room, go left as far as you can, and then travel south, through the door. Here, go to the left and travel up a center path which has many rocks making it maze-like. At the end is a sign that says, "Falling Rocks." Completely disregard this sign and use Force on the stump behind it. When it falls, an enormous boulder drops from the sky, and after a short cutscene subsequently smashes an equally enormous hole in the floor. Climb down the ladder on the left side, then slide down the wall. The railroad track is now broken, so you can use it as a ladder to descend. In here, the appearance of the area completely changes; save now.
REAL Boss Battle: Hydros Statue
The leader of all the little living statues that were flooding the town. It is obviously water-based, so Mia's Psynergy and Mercury Djinni are fairly worthless. Use her as a healer (she should be around level 15, and thus have learned Wish, a full party healing move.) Surprisingly, Fire attacks are especially effective against it. Ragnarok is a good move to use while Djinn are recovering, and so is Heat Wave. As usual, make full use of your Djinn's abilities and summons. Zephyr is always useful to get your party members to attack first. Save Quartz for an emergency, but Granite can prevent a lot of potential damage from being taken.
After it is defeated, the statue will crumble, revealing a treasure chest. Inside is the Lifting Gem, which grants the Psynergy Lift, a very important skill.
Backtracking to the 2nd level mines, if you follow the tracks from the entrance you'll come back to a room where a chest was blocked by a boulder previously. Using Lift you can now open the chest for a Cookie, an item which permanently raises your max PP.
Now return to the mine's lower floor entrance, walking down to the split in the rail tracks again. When you see a boulder, use Lift to move it out of the way. Walk under it and go through the door.
In this room, go down the left path and Move the stump to enter a room with a chest containing a Vial. Backtrack down the center path and use Lift again to remove a boulder, which will take you to the exit of the mines, just outside of Lama Temple.