After completing the Dragon's Den, you can enter a challenging 'monster rush' in the Soul Shrine, which is located north of Mobliz. You can also re-enter the Dragon's Den, and at the end, will be another powerful optional boss...

Levels vary, since levels aren't really a reliable measure of strength in FFVI. I got through the Dragon's Den with characters whose levels were in the 30s and 40s, others will suggest leveling up to the 50s and beyond. It all depends on your spell and equipment setups.

I greatly recommend getting the Lightbringer sword (bet the Ragnarok sword in the Coliseum), and uncursing the Cursed Shield into the Hero's Shield. You can get both the Ragnarok and Cursed Shield in the locked houses in Narshe with Locke in your party. To uncurse the Cursed Shield, you must fight 255 (or possibly 256) battles with it equipped. While equipped, it lowers your stats and inflicts every negative status effect on the equipped character. Equip that character with a Ribbon to negate all the statuses except a lengthly countdown timer. Both the Lightbringer and Hero's Shield give great boosts to all stats, especially Magic and Physical Evasion, and the Hero's Shield in particular can absorb all elemental attacks. It just takes awhile to uncurse it...fight in the Solitary Island to remove the curse quickly.

Party selections differ from player to player. While Gau is generally considered the most powerful character in the game due to broken equipment and Rage setups, the fact that he is uncontrollable while using Rage makes me take him out of my final parties. Umaro is similar, since all he can do is attack. I am fond of using Relm (highest base Magic), Strago (useful Blue Magics), Mog (no encounters), Celes (Runic to absorb dangerous spells), and Locke (powerful attacker with Genji Glove/Master's Scroll) to be very useful. But any party setup should be just fine with the right equipment and spells.

Great Relics are Ribbons (negate all negative status), Soul of Thamasa (found on top of the Fanatics' Tower, allows you to cast two spells in a row), Gold Hairpins (halve MP consumption), Celestriads (formerly known as Three Stars and Economizer, reduces MP costs to 1), Molulu's Charm (gets rid of all random encounters, but can only be equipped by Mog). There are probably others that I'm forgetting, but Ribbons and Celestriads in particular are almost necessary for survival against the more annoying foes.

Pack plenty of Teleport Stones so that you can make an easy escape in case you need to regroup or restock on supplies. Buy plenty of Hi-Potions, Ethers, and Tents to heal between battles. Make sure to save often, some random encounters and chest battles can be devastating if unprepared (not to mention the secret bosses). Make use of Golem and Mighty Guard. Other than that, be prepared for a decently long and tedious bonus dungeon, with some annoying puzzles and bosses.