Old School Player
Start in old school mode (no map, you need to choose this when starting a new game), has to be normal difficulty, but you may create your own party.
You have to finish the map "at risk" in this setting

Born of the Adventure
Finish the tutorial level

Into the Dark
Finish the first level

Acrophobia
First time fall in the a hole trap (just jump into 1 of those pits)

Secret Searcher
Find a secret place (for secret places, they're pretty simple, most of them are behind a button on the wall, turn on the map to see how many secrets are on that floor and how many you found)

Dungeon Map Master
covered 90 percent of the dungeon tiles (just check map and walk all over the place even if room explored but not stepped on every tile, look at traps, gates and statues to visually unlock the tile too)

Penny Pincher
Quit tavern without spending a penny (just go in and out)

Spending Money Like Water
Spent 100 000 gold in one shopping time

Up Start
Carrying 200 000 gold

Senior Beggar
Wearing a set of beggar suit (equip a full set of rags on a character, should be easy to find, but also sold in shop)

Arm to the teeth
All characters wearing armors (all 4 characters wearing at armor pieces in every armor equipment slot)

Elite Archer
Put on a set of archer armors (ranger armor set works fine, you can even purchase it in shop, just equip the whole set on a character)

White Wizard
Get the set of Wizard Suit (equip a full set of the white mage armor, they're called arcane hat/shoes...)

Treasure Hunter
Get the three kinds of magic sword (fire sword, poison sword and ice sword, can be found in last few levels, but can be bought in shop much earlier)

Unassailable Armor
Get the set of General Suit (ditto, items are literally called general hat/shoes...)

Essence of magic
Get the best magic weapon (Fine orb (crystal ball) being equipped will unlock it)

First Blood
Kill the first monster

Dungeon Sweeper
Kill 50 monsters

One Hit Kill
Kill a monster with only one hit (if you have trouble doing this, progress through the game and return to a lower levels arena, be wary of level transfer where you can't go back)

Apprentice Mage
Cast a spell

Guardian Angle
Resurrect a player (clerics life magic lvl 5 will unlock the spell)

Learning Master
Learned at least 5 kinds of skills for one character

Save All Or Destroy All
First time finish the game

Admirer
At the tavern keep clicking at the witch, I believe you need a 100 responses from her to get the achievo, just leave an autoclicker on her face, go eat. (thx djct™ for the tip)

Story Teller
<<Fixed since 20th December update>>
You must find all the letters across the whole game.
I'm not sure whether it's just story letters or all letters or whether you have to keep them in your inventory, I did find all and keep them all.
Total amount of letters is 35
(I deleted the list of letter locations from long ago, so if you have a list, I'll edit it)

When you'll find a room of pressure plates and a letter stating "rune of air" or another, just place something on pressure plates in this design, in case you're not carrying scrolls to see the symbol.

Rune of fire
x o o
x o o
x x o
x o x

Rune of air
x x o
x o x
x x o
x o o

Credit to 小河边 guy, however you read that moonspeak, for the rune display.