Greetings!
Most of the achievements in this game are quite simple and self-explanatory.
So, in this guide, you can find tips and tricks for the most difficult achievements (:
Leeet's go!

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Adventure: Any
Node: Dark Knight with a purple flag
Event: Dark Army Checkpoint
Party: Based on magic damage

You should choose "Fight them" option.
Combat is easy: the Dark Knights have low health, and the mages kill them with one shot.

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Adventure: Stormcloud's Winter
Node: Troll Champion Combat

There are two events with barbarians: with 2 and 3 of them. Just make your path through as many required nodes as possible.
To get this achievement at least one barbarian must be alive at the end.

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Adventure: Stormcloud's Winter
Node: Any Combat with an enemy that can freeze your hero

For this achievement you must break ice (with combat props or attacks) before the frozen unit's turn starts and ice shield dissappear.

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Easy with Asra and her "Shield of shadows": just kill all but one low hp enemy, then let him kill the rest of the party, trigger Shield and finish combat.

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Node: Any with Obelisk
Party: Bombardier

Kill everyone, wait for the Obelisk to spawn 5+ tentacles within 1-Hex and attack with Bombardier.

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Round is all your heroes and enemy(!) turns, which are between banners in the turn schedule at the top of the screen.
Personally, I got this achievement with Reg'son, Bombardier, Orc Cleaver and Ranger in the boss fight in "Stormcloud's Winter" adventure.
The scenario was something like this:
~8+ damage from Bombardier bomb planted on previous round
~8+ damage from Bombardier attack on two enemies
~22+ damage from Reg'son, Orc Cleaver and Ranger attacks
~14+ damage from Orc Cleaver counter-attacks

But I think there's a much easier way to get this achievement but I didnt test it :D
Look for the Obelisk node, and again spawn many many many tentacles xD
Theoretically Bombardier can deal 20-35 damage on 5-7 targets.
Also you can use Barbarian to deal another 10-20 damage on 2-4 target.
Remaining damage can be dealt by two another heroes in party.
Seems easy^^

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Adventure: Extradimensional Menace
Node: Weaponsmith and 300+ gold in the pocket (:
Difficulty: Casual

In this adventure, you will receive the "Sharpening stone".
Visit a weaponsmith (having 300+ gold) and upgrade any hero 2 times.
After that use the stone on the same hero.

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Adventure: The Wild Moon
Node: The Sylvan Elf Hall
Party: 4 ranged heroes

Maybe someone got this achievement at random or with lucky dices, but it wasn't me :'(
So here's a plan:

Take 3 ranged heroes in party, and then visit "The Sylvan Elf Hall" at the middle of the map.
Recruit another ranged hero (if you haven't already) and head to Archery Contest. All heroes will participate.
After that pray to RNGesus, and if you're not lucky, just press ALT+F4 and try again.
I got 4 dices only on my fifth attempt^^

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Adventure: Krum'Thak's Dominion
Node: Orc Champion Combat

You need to get encounter with 3 knights in the center.
Save at least one of them to get achievement.

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Adventure: Extradimensional Menace
Node: Demon Lord Combat

You need to get encounter with villager, who changed his mind about selling his soul xD
Actually this peasant dies quickly if you dont kill enemies around him, so take Gerald or Knight in the party to provide some shields (:

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Adventure: Stormcloud's Winter
Node: Winter Wolf Combat

I recommend reloading the adventure if the required nodes are close to the beginning or end of the map.
If its close to start - you have a big chance to get a simple combat with 3 wolves.
If its close to end - you have big chance to get a tough combat with wolves and Yeti.
You need to get encounter with 2 villagers near the van. Save them both.

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Adventure: Stormcloud's Winter
Node: Argalem Combat

You need to win 3 types of Aragalem combats:
- in the pub
- in the village
- with Yeti

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Adventure: Stormcloud's Winter
Node: Argalem Combat
Party: Reg'son, Bombardier, Orc Cleaver

You must get trolls in the village encounter and kill everyone before mages come to your aid.
So here's strategy:
In the beginning deal as much damage as possible with Bombardier bomb (3-4 enemies).
Orc Cleaver should tank and counter-attack, so send him to a group of melee enemies.
Reg'son is damage dealer with high speed, so use him to kill big orcs and clean up far-reaching enemies.
The fourth hero is necessary, but its random.. and I got Witch Doctor ....... :D
Good luck!

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Adventure: The Wild Moon
Node: A hut with a purple flag
Events: A Dialogue With The Stars, As Darkness Falls
Party: Bruxa (required), Arcane Wizard (optional, for magic damage), Knight (optional, for defense)

Definitely the most interesting achievement in the game!
First, pay attention to the constellations in the lake.
Its bat, serpent and bear.
You need to get "A Dialogue With The Stars" event at the required node.
Choose "Examine the Ashervan witch" option.

Now Bruxa can help you - choose "Translate her ramblings" option.
You will receive the amulet as a reward. Don't discard this item and keep it in the inventory.

Next step is getting "As Darkness Falls" event. It's a random encounter, which triggers when you travel between nodes. I believe that when you have amulet in your inventory, this event is no longer "random", and sooner or later you will get it.
In this event you must use amulet (choose "It glows.." option).

Then follow the constellations (from the lake): choose "Bat", "Serpent" and "Bear" options.
Eventually you will reach Ashervan den (its a pretty tough combat here). The achievement will pop up after victory in the combat.

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Adventure: Any
Node: Wizard with a purple flag
Event: The riddlemaster

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Adventure: Krum'Thak's Dominion

Here comes my favorite easter eggs^^
You need to find some characters on the adventure map, so if u dont have one, just go back to the atlas and return to the adventure: the map will be refreshed.
For this achievement you need to tap and break two pigs houses (third one seems indestructible xD).

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Adventure: Krum'Thak's Dominion

Click on the pink bear.

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Adventure: Krum'Thak's Dominion

Click on the well.

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Adventure: Krum'Thak's Dominion

Good old sheep explosion :D (no)

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Adventure: Stormcloud's Winter

Click on the white wolf.

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Adventure: Extradimensional Menace

Click on the vampire killer.

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Adventure: Krum'Thak's Dominion

Click on the alien ship.

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Adventure: The Wild Moon

Click on the ninja.
Unfortunately, the ninja spawns in a random part of the map, so watch carefully. ^^

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Adventure: The Wild Moon
Node: Orc Warrior with a dice
Event: Orcish Deforestation

Choose "Fight them!" option.
To make it easier, take heroes with stun / root, and immobilize enemies near aggressive trees :D

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Achievement is easy, I just wanted to show list of "Elite" enemies^^

I hope this guide was helpful and interesting (:

Thank you for attention, have fun <3

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P.S. Special thanks to all of you who award this guide!