You need reach level 15 to start those quests.
Town 2
Knight
1-Kill some monsters in Map 5 at any difficulty
2-Kill some monsters in Map 3 at any difficulty
3-Talk to the Accessory shop owner in Town 2 (Jewel in the world map)
4-Clear Map 2 on Very Hard in 8 minutes or lower
Magic Knight
1-Clear Map 4 on Hard in 10 minutes or lower
2-Get 30 drops from mages in Map 1 on any difficulty, 10 drops from Map 4 in any difficulty, and 5 MP potions that can be purchased from the alchemist.
3-Clear Map 6 on Hard or above with B rank or higher
4-Clear Map 6 on Very Hard to get a drop
Sword Knight
1-Clear Map 4 on Hard in 10 minutes or less
2-Clear Map 6 on Hard with B rank or higher
3-Kill 14 bats in Map 2 at any difficulty, Kill Poison bees in Map 1 at any difficulty, and Kill 2 batkings in Map 2 on Very Hard
4-Get a drop from a mini-boss in Map 6 on any difficulty
Magician
1-Clear Map 5 with B Rank or higher on Hard
2-Get a drop from the red magician mini-boss in Map 1 on Very Hard
3-Get 2 drops from the boss in Map 6 at any difficulty, and 2 drops from the boss in Map 4 in any difficulty
4- Get 30 drops from mages in Map 1 on any difficulty, 10 drops from Map 4 in any difficulty, and 5 MP potions that can be purchased from the alchemist.
Dark Magician
1-Get a B rank or higher at Map 6 on Hard mode (**).
2-Collect 18 item drops from Bats in Map 2 and Collect 1 blue elixer. (can be bought at alchemist for 1k)
3-Clear Map 3 on Hard mode (**) taking 20 or less hits.
4-Speak to Hoffman (guy in center of town).
High Magician
1-Get 30 drops from mages in Map 1 on any difficulty, 10 drops from Map 4 in any difficulty, and 5 MP potions that can be purchased from the alchemist.
2-Get 1 item from the Alchemist shop (costs 1000 ED) and get 10 drops from any dungeon in the second town.
3-Clear Map 3 on Hard while getting 20 hits or less.
4-Talk to the Alchemist in Town 2
Ranger
1-Clear Map 5 twice
2-Collect 10 drops in Map 3 and Kill 18 monsters in Map 4 at any difficulty
3-Talk to the weirdo guy located in the middle of Town 2
4-Kill the 10 light wisps in Map 1 at any difficulty
Combat Ranger
1-Talk to the Accessory shop owner
2-Kill 8 monsters in Map 3 and the boss in Map 2 at any difficulty
3-Clear Map 6 at any difficulty in less than 8 minutes
4-Get B Rank or higher in Map 6 on Hard, and Get B Rank or higher in Map 5 on Very Hard
Sniping Ranger
1-Talk to the guy in the second town(Sword Icon)
2-Get 2 drops from Map 6 on any difficulty
3-In Map 2 dungeon 1, Kill 18 of the blue headed mushrooms
4-Get a B rank or higher at Map 5 on Very Hard mode (***) and a B rank or higher at Map 6 on Very Hard mode (***).
Taker
1-Kill some monster on Map 5 on any difficulty
2-Talk to the Alchemist in town 2
3-Clear Map 3 on Hard a few times
4-Clear Map 1 in Very Hard in 7 minutes or lower
Sword Taker
1-Kill some monsters in Map 4 in any difficulty
2-Talk to the Weapon seller in town 2
3-Clear Map 5 on any difficulty for a drop (quite rare)
4-Get a drop from Map 6 on any difficulty
Over Taker
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Another Code
1-Clear Map 5 twice at any difficulty
2-Clear Map 1 on the very hard (***) difficulty, and kill the giant red magician.
3-Obtain B rank or higher in map 3 (I forgot which difficulty, Im pretty sure its hard (**) )
4-Talk to the Alchemy NPC in town 2
Code Architecture
1-Get a random drop from the bats in map 2 (any difficulty)
2-Get a random drop from map 4 (any difficulty, but highest one recommended)
3-Get a random drop from map 6 in hard (**) difficulty
4-Complete map 6 in very hard (***) in 15 minutes or lower
Code Exotic
1-Clear Map 2 in any difficulty
2-Clear Map 4 twice and Map 6 in any difficulty
3-Collect the spanner from a well in Map 4 in any difficulty, and 20 rocks from breaking/disassembling weapons
4-Clear Map 6 on Very Hard in 15 minutes or lower