Thabes Labyrinth is an enormous dungeon which tops at 10 levels --- well, more like, 10 basements. Every time you go one level further down, the strength of enemies increases.
Basements 1 - 4 are quite simple; be careful of Shadow/Devil weapons, however, since they can deal some damage if your units aren't capable enough. This is a decent place to grind.
After Basement 2, you should probably get used to Venin Claws (poisons a unit if the Terror hits while attacking or counter-attacking), Numbing Claws (disables movement for who knows how long if the Terror hits while attaching or counter-attacking), etc. Poison causes a unit to lose 10 HP/turn so be careful.
Basement 4, get ready for some dragons, which aren't too bad since they don't have a large range, but still be wary.
Basement 5 gets a bit harder; this is the midpoint of the dungeon, and the only thing standing between you and the real deal is a couple of soldiers... and a Fire Dragon. Yeah, no biggie, but if your units aren't capable, this dragon will wipe them out with its large Mt and range. Just be careful and you'll do fine. Also, be PREPARED for crazy good Entombed Terrors. Their crit rates are pretty high (maybe around 17% for me), so be careful when dealing with them, plus high attacks. Their Def and HP is low, so don't be afraid to take them out with Gradivus or another 1-2 range physical weapon.
Basement 6: Immediately, enemies will have ??? amounts of HP, with ratings at least 170. Most enemies will have Rusted weapons, but some will have Venins (same concept as Venin claws), so just be careful when sending units out to fight. All in all, not that hard, just watch your units' HP and make sure they don't fall too fast. Another one, Eerie Screech, on gargoyles prevents units from using magic/healing if they hit during an attack or counter-attack.
Same concept for Basements 7-8, it just gets harder each time.
Basement 9: The appearance of those strong Entombed will be more frequent; get ready for that. Also, towards the end of it, dragons. Get. Ready. For. Crazy. Dragons. Don't get caught off guard. Take note of their range, and you pretty much want to kill them the moment you attack. Once again, towards the end of Basement 9, you may spot a part of the wall that's crumbling:
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Yes, there are two sacred springs in there, but see that enemy right be hind the wall, and just stalking at the entrance? That's a dragon. So unless you want to face maybe 20 dragons (not too sure how many, just that there is A LOT) all at the same time for the springs, you might want to avoid that area. But if you do decide to go there (like meh), just be ready.
Basement 10: Honestly, the only enemies you'll encounter is the fight with _____. (In case there's some of you who don't want it spoiled for them.)
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Like in the battle with Jedah, I would once again recommend you to bring along some Blessed weapons. They offer good crit rates, restores 5 HP/turn, and can help with hit rates. Brave Swords are highly recommended, since critting is pretty essential in this dungeon. If you can, I'd also advice the use of Gradivus. It's one of the three Regalia, plus range 1-2, high Hit, and Mt of 13. The only bad part about it is its weight, so be sure to equip it on a high speed unit.
I'd also recommend you to take advantage of the Evacuate order. You probably shouldn't run in and expect to make it all the way through (the first time, I made it to Basement 9, only for Celica to be wiped out by the dragons behind the cracked wall), because if Alm/Celica die, all the EXP that you earned and all the progress you've made made will be lost. It is impossible to save while in the dungeon (except for bookmarks, but those don't count in this situation). By evacuating, it is possible to keep all the EXP and progress you've made; when you re-enter, you'll be even more ready. Don't worry, the places that you've gone through will still be visible on the map. (You can evacuate everyone at the same time via evacuating either Celica or Alm; who's ever in lead.)
I definitely advice leveling up to at least level 15 for a units' highest promotional class (i.e Dread Fighter, Saint, Falcon Knight, etc.), and even better, overclass by use of DLC (only optional; not necessary). And even, even better, would be if you could reclass a unit back down to Villager, and then continue back up to that promoted class. You don't have to do this for everyone in your team, if you don't want to. I only used four main units, and by the end of everything, here were their stats:
