All these achievements are story related and can't be missed.

Absolutely Legal
Use Ether Inhaler


In the tutorial you have to destroy an explosive barrel which will hurt you. The Ether Inhaler is one of the medical items you'll have to use to treat your wounds and continue the tutorial.

Watch Me Rise
Complete the tutorial


As the title says, complete the tutorial.


There are two endings in this prologue:

(1)
Bella Lugosi is Dead
Disrupt Archon’s ritual


Archon is the boss of this prologue. The achievement is awarded after defeating him (destroy the statues).

(2)
At What Cost?



As your friend says, run away out of the church. Archon will transform into a gargoyle. Defeat him for the second ending and another achievement.


Last Hope
Find the Stoneshard


After killing Archon (the boss) go out of the church. The shard is lying in a hole between the three guys you just rescued. Take the shard and put it in your inventory.

That's Brutal!
Die during the tutorial


The easiest way to do this is to stand in the range of the explosive barrel when it explodes. (Marked red on the floor)

Comeback!
Have your health reduced to 1 point, survive and restore it back to at least 50%


The difficult part is to get 1 hp. Use enemies or traps for this, but make sure to survive the encounter and find a save spot. Press B on your keyboard and chose the rest mode to heal yourself. Stop bleading before this or you'll die.

Dressed to Kill
Equip an item to every slot. Rings and amulet slots don’t count


As the description says, equip an item in every slot, except rings and amulet. Search every chest and shelf for this, nevertheless you may do multiple runs because loot spawns randomly and you may have runs where you don't get everything.

Legalise Drugs and Murder
Kill any enemy while experiencing Bad Trip


Bad Trip is a status effect you get after consuming the Herbs Extract, or with a little chance, by Stardust. Simply kill an enemy while having this effect active.

Dear Diary...
Collect and read all 5 diary pages


Locations of all 5 pages:


1 In the tutorial in the right shelf

2 & 3 After you finished the tutorial and jumped through the hole in the floor there is a wardrobe with 2 pages

4 After going down the stairs into the next area you'll find a bonfire and a backpack with page No 4.

5 After going up the stairs into the next area, the church, you'll find page No 5 on a bench in front of the boss.

Right click and read them all!

Bad Luck Vampire Extravaganza
Kill at least one vampire of every type


You have to kill one of every vampire (except the boss) in one run. This may take some tries, because everything is spawned randomly and you don't always encount every type.
According to the devs, you have to kill these 6 lads in one playthrough:

General Tips:

• Use Rest Mode to heal and restore mana as often as possible.
  
• Don't forget to eat and drink, every status effect has an influence on your stats.
  
• Doors are your friends and can't be opened by enemies. Make this to your advantage.
  
• Kill everything to gain as much XP as possible

Tips for boss fight (from my experience):
Since everything is randomly generated you might not get everything

Preperation:

• Two handed weapon for higher damage prefered
  
• Skilling Agility for higher evasion rate
  
• Having at least one potion for healing
  
• Use lightning spell to enchant your weapon before the fight (don't forget to rest and restore mana)

Fight:

• Your main goal is to destroy the statue, the skeletons won't hurt that much if your evasion is high enough.
  
• Stay directly in front of the statue, step aside if they enchant the floor, get back directly in front, but don't get closed in by the skeletons.
  
• Focus statue with melee attacks, use firespell to damage statue and skeletons

But mainly have fun and don't rush, you can take all the time you want :)