Every main story dungeon up and including Corridor of the end will have a secret tunnel on 4f of that dungeon (unless specified otherwise), that looks similar to this:

Press the attack/jump button on these spots, and you'll be able to enter an optional 5th floor with a bunch of extra chests.

If you clear a dungeon below the clear time, you'll get 1 fame for each second you were under the clear time.

Talking to Grampiyo at specific fame milestones will net you certain unlocks.

• 5 fame: 1 Gold.
  
• 10 fame: Unlocks entry to Hiyo's ship.
  
• 15 fame: Unlocks the job change npc on Hiyo's ship.
  
• 30 fame: Gives a free widen artefact, adds widen's for sale at the shop npc on Hiyo's ship.
  
• 50 fame: Adds the MAD RAT HEART MML to the mml vending machine at the top right of Hiyo's ship.
  
• 70 fame: Adds the MAD RAT, ALIVE? MML to the mml vending machine at the top right of Hiyo's ship.
  
• 100 fame: Adds the Cladun X2 songs to the shop on Hiyo's ship.
  
• 120 fame: Adds the Cladun 1 songs to the shop on Hiyo's ship.
  
• 140 fame: Adds the Legasista songs to the shop on Hiyo's ship.
  
• 200 fame: Allows the hidden map vending machine on the top right of Hiyo's ship to sell you dungeons.

Once you get 200 fame, you can buy dungeons from the hidden map vending machine.
I'd recommend stacking a bunch of magic power on merchants gold drop up ability, then running through ran-geons/map-geons to farm the gold you need for these.

• Purgatory floors 1-8, Purgatory 2 is a great place to farm exp in the early-mid postgame, I'd suggest using wave slash to clear out the enemies, including the enemies below the exit.

Special note here, when you defeat the boss on a dungeon you haven't cleared yet, you're guaranteed a drop. As a result, you may wish to retry these fights a few times to try for some good gear/artefacts.

• Challenge: The Mask (Lv. 100-500)
  
• Challenge: S. Mask (Lv. 1000-9999). S. Mask lvl 1000 is the actual best place to farm exp in the game, you'll need 200 fire resist and 4000 or so atk/def. Enter the boss area, head down, then farm the summons.
  
• Wave dungeon 1F-4F: Clear S. Mask (Lv. 1000) to unlock.
  
• Challenge: Karina (Lv. 100-500)
  
• Challenge: S. Karina (Lv. 1000-9999).
  
• Challenge: S. Mask & S. Karina (they're both lvl. 9999)

Postgame only, Jellia is at the top of the town.

• Versus Jellia (Lv. 100), talk to Jellia with >=30 hours on your current save.
  
• Versus Jellia (Lv. 500), talk to Jellia with >=50 hours on your current save.
  
• Versus Jellia (Lv. 1000), talk to Jellia with >=70 hours on your current save.

Postgame only, These need to be unlocked in order, but you don't need to clear the previous dungeon to do so, unless specified otherwise.
Talk to Stabitha by going behind the counter in the weapons shop for these. Remember you can buy magic power artefacts from this very shop with the Sorcery titles you need.

• Versus Dark Glutton (Lv. 500): Give Stabitha an artefact with Sorcery 3 on it.
  
• Versus Dark Glutton (Lv. 1500): Give Stabitha an artefact with Sorcery 4 on it.
  
• Stabbing Stabitha (Lv. 9999): Give Stabitha an Artefact with Wizard SP+140 on it.
  
• Villainous Showdown 1f-4f: Give Stabitha an Artefact with Shaman SP+200 on it.
  As advertised, every story boss, optional boss and high ranking enemy is gathered here. It's a great place to farm double zero's/twin's if you can handle it, and beating 4f with stronger enemies on gives a particularly good magic circle
  
• The Bird Cage 1f-4f: Clear Versus Dark Glutton (Lv. 1500).
  This place is brutally difficult, it's 1-2 rooms full of dangerous, high-tier monsters who will swarm over you. It doesn't unlock anything, but the sheer amount of high tier monsters makes it a great place to farm high rank gear and artefacts, if you have the stats and elemental resists to survive.

You need to talk to Ares on the left of the town for these, and the unlocks need to be done in order.

• Vs, the Twin Dragons (Lv. 200): Give Ares a weapon with >= 160 quality.
  
• Evil Dungeon (Lv. 2000): Give Ares a rank 20 weapon.
  
• Brutal Dungeon (Lv. 3000): Give Ares a rank 23 weapon. This doesn't unlock anything, and the loots pretty bad by the time you can get one of these, so thing carefully if you want to throw away a rank 23 weapon for this.

These are just as described, postgame dungeons providing more of the kinda dungeons you've seen in the story.

• Dungeon Most Bizarre 1f-16f: In the postgame, talk to Hodrick 4 times.
  
• Mega-geon Seal: unlocks after clearing Dungeon Most Bizarre 16f.
  
• One More Dungeon 1f-16f: unlocks after clearing Dungeon Most Bizarre 16f. 3f and 4f are bugged, you have to set your max fps to 60 or lower to be able to clear them.

After clearing Mega-geon Seal, You'll unlock the Mega-geon, it's like a regular ran-geon, with a bunch of crucial differences:

• The enemies are way stronger. A lvl 1 enemy here is equivalent to a level 5000 enemy in a regular ran-geon, and they get harder fast.
  
• There's seemingly infinite floors, and the floors are all comprised of random rooms from ran-geons and map-geons that would appear at that floor, pasted together.
  
• Every time you enter an angel, fallen angel, demon, hell or abysmal gate, you might randomly lose 1 or more points in all your resists for the rest of the run. Enter a normal gate to restore them.
  
• Hiyokki's are more likely to appear.
  
• Gear at rank 21 or higher can still be strengthened by the enhance gates here.
  
• Gear can also be enhanced past 999, up to 9999.
  
• You can get the full variety of top tier, ultra rare titles here, combining the effects of 3 or more titles.
  
• Whenever a double twin/zero/widen would drop, there's a chance you'll get one of the Yggdrasil artefacts instead. This also applies to regular ran-geons and map-geons with stronger enemies on, but you only get the first 2 that way, while the mega-geon can drop all 5 types.