Ziggurat

Arno the Apprentice
Starting Character.

Kraz the Novice
Unlocked with 200 Wand Kills
Wand kills are your basic weapon and 200 should come naturally over your first couple of games.

Menzi the Shaman
Unlocked by killing 40 Shaman
Shaman are the hooded guys who summon Carrots.

Simon the Sorceror
Beat the game once.
You must complete 5 floors, you can hit Y at character select to place the game on easy.

Algorab the Alchemist
Deal 35,000 Alchemic damage.
Alchemy weapons use Orange Mana and appear in slot 4.

Rigel the Acrobat
Deal 15,000 Staff damage.
Staffs use Green Mana and occupy your 3rd slot.

Saiph the Librarian
Deal 25,000 Spell damage.
Spells use Blue Mana and are homed in slot 2.

Corvus the Vampire
Defeat 5,000 creatures.
Unlocks naturally whilst trying to complete the game with all characters.

Osuna the Bard
Defeat 250 Kobolds
Kobolds are the grey crossbow wielders who fire little white bullets at you. You can wait til it comes naturally or try for an Obelisk Room that spawns Kobolds.

Hadar the Templar
Kill 25 Demons
They look like tall humans who fire red balls of energy at you, they appear on floor 4 onwards and the final boss spawns them.

Jules the Harlequin
Find and open 10 Mystery Boxes.
Mystery Box Rooms appear as little Treasure Boxes on the map and have a square box in the middle that will spawn various treasure or monsters. There is a Perk that you can acquire that increases the frequency of these rooms, but you'll typically find one or 2 per run.

Cid the Seer
Kill 250 Carrots
Walking angry carrots... Shamans spawn them and they spawn in Obelisk rooms if you wish to farm them.

tip:
One of the bosses is a Poloko the Shaman, it spawns both Carrots and Kobolds if you wish to farm either, but it might be easier to wait til you find an Obelisk room that spawns either or both.