Everdell has 18 achievements, most of which you should unlock just by playing for a while. I've added some specifications on the requirements along with a couple of tips for most of them.

As far as I'm aware, all achievements (excluding those whose descriptions state otherwise) can be unlocked in either online matches or when playing versus AI, but not in local multiplayer matches. They can also be unlocked in challenges, some of which provide rather big advantages when going for certain achievements. I'll do my best to mention such opportune combinations.

Instead of unlocking right away, all achievements should be unlocked at the end of the match they were gained in.

These achievements relate to utilizing the effects of specific critters or constructions.

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Dining Duo
Pair a harvester and gatherer.


When your city contains a Harvester and you place a Gatherer (or vice versa), they can be combined into a single critter, enabling both of their effects while saving space.

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Leader of the Flock
Score 3 victory points in a single game with Shepard.


The Shepard's ability allows you to gain 1 victory point for each victory point token placed on your Chapel.
A victory point token is placed on the Chapel whenever a worker is deployed to its location. As the Chapel only has 1 slot for workers, you'll ordinarily have to send one worker there in spring, summer and autumn, before playing the Shepard to unlock this achievement.

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Dungeon Master
End a game with 2 Critters in your Dungeon.


The Dungeon allows you to remove critters from your city in order to reduce the costs of a card you want to play.
It starts of with only one slot for this, requiring the Ranger to be played in order to unlock the second slot. Once you've got both cards in play, simply make sure to have two critters in you city, then place two Constructions, each time using the Dungeon's ability. Also make sure to not remove the Dungeon, e.g., by using the Ruins.

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Path of Enlightenment
End a game with two workers in your Monastery.


The Monastery allows you to send workers to it in order to gain victory points, with the workers staying in the Monastery even through season changes.
Initially, the Monastery has only one destination slot, requiring the Monk to be played in order to unlock the second slot. After unlocking both slots, send two workers to the Monastery and make sure to not remove it before the game ends, e.g., by using the Ruins.

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Tree Hugger
Score 5 bonus points in one game with Ever Tree.


The Ever Tree gives you 1 victory point per Prosperity card in your city.
You'll simply have to have 5 other Prosperity cards placed in your city before placing the Ever Tree. Potential cards for this are the Architect, King, Gatherer, Palace, Castle, School and Theater, most of which can only be placed once.

Next up are achievements for which you'll have to construct your city in certain ways.

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City Planner
End a game 15+ cards in your city.


15 is the limit for how many cards can be placed in your city, with certain cards like the Wanderer allowing you to exceed this limit. Simply place as many cards as possible to earn this achievement.

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Full House
Have 5 or more occupied constructions in a single game.


Each construction has a corresponding critter which can be placed for free if you have the construction in your city. Simply use this feature with 5 different constructions, making sure you have enough space for the 10 cards this achievement will require overall.

These achievements will see you repeatedly using certain actions during your turns.

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Show-off
Take 5 or more turns in a row.


For this achievement, you're required to be the last person to pass at the end of the game, leaving you as the only one still allowed to make turns. With that, simply make sure to ration your resources so you can take at least five more actions before passing yourself.

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A Great Journey
Journey three times in a single game.


You can only send workers on journeys during autumn, meaning you'll have to make sure to have 3 spare workers saved for this. As long as you do this, you really can't fail this achievement, since the 2-point journey is shared and thus always available.
The "Late Start" challenge starts you off in autumn with 18 workers at your disposal, making it a great way to force this achievement.

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Patron
Send a worker to an open destination owned by another player 3 or more times in a single game.

This one is of course very reliant on other players placing constructions with open destination fields, namely the Inn and the Post Office.
Try to send workers to such destinations as soon as possible, to avoid other players hogging the limited slots. Also, keep in mind that the workers will be removed from the destination fields whenever the player owning them prepares for the next season, giving you another shot to send your own workers there.

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Holiday Season
Claim 4 or more Events in a single game.


There are just 4 basic and 4 special events available during each game, meaning you'll have to claim at least half of them.
Try focussing mostly on the basic events, as their requirements are much less specific then those for the special ones. For the special events, keep them in mind and try to work towards their requirements when possible. Since they're harder to claim, they're also less likely to be snatched away by your opponents.
To make this achievement easier, consider playing with fewer opponents to reduce the risk of others snatching events before you can claim them.
When playing the "Guest List" challenge, all cards required for special events are present on the meadow, potentially making this achievement easier to obtain.

For these next achievements you'll essentially just have to play well.

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Competitor
Win an online game.


As the description states, you'll simply have to finish an online game as the winner. The game is only counted if all players stay until the end of the match, without any being replaced by AI.
In spite of the description, you used to be able to unlock this achievement in offline play against AI prior to patch 1.1.8.

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Seasoned Competitor
Win 25 online games.


Like with the last one, you need to win a game without any players leaving mid-match and being replaced by AI for it to count towards the 25 goal.
Similarly, this achievement could be obtained in offline play against AI prior to patch 1.1.8.

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Half Centennial Club
Score 50 victory points in a single game.


Like the description states, you simply have to end a game with 50 or more victory points, no matter if you end up losing or winning.

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Three Quarters Club
Score 75 victory points in a single game.


Just like for the previous achievement, simply end a game with 75 or more points. It doesn't matter if you win or loose.

And lastly for the base game, achievements related to the completing certain additional game modes.

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Graduate
Complete the Tutorial.


As the description states, simply play through the three short tutorial stages without skipping. You can access them again through the main menu in case you did skip.

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Challenger
Compete every normal Challenge.


Challenges are Everdell matches against bots with changed rulesets, forcing you to adapt the way you play. You'll mostly have to figure out the optimal way to play around the respective rule changes.
It appears that with the release of the Glimmergold DLC, this achievement now requires you to complete both the base game and DLC challenges.

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Ultimate Challenger
Complete every hard Challenge.


The hard versions of the challenges add more AI opponents and tighten the different rule sets further. They're unlocked after beating the respective regular challenge.
Like the previous achievement, this one apparently requires you to complete all base game challenges as well as the ones added in the Glimemrgold DLC.

Everdells's first DLC Glimmergold introduces 5 new achievements related to the three smaller expansions it contains. Unlocking these requires you to own Glimmergold and activate the respective expansion by ticking the boxes on the match setup screen.

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Juggling
Reveal 3 or more cards in a single use with the Juggler.


Added with the Extra! Extra! expansion, the Juggler allows you to choose between two effects when playing it, the first of which allows you to spend 3 wood in order to gain 3 victory points. The second effect is the relevant one for this achievement, letting you temporarily draw as many cards as you want for one wood each and rewarding you with 6 victory points if the cards drawn are worth at least 6 victory Iit doesn't matter whether you cross this six point threshold for the achievement - you merely have to draw three or more cards.
Using the "Extra! Extra! Extra!" challenge, which doubles the amount of Extra! Extra! cards present in the game, will make it a lot easier to receive the Juggler card.

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Scurrble Championship
Have three Scurrble Champions and a Scurrble Stadium in your city.


Available through the Extra! Extra! expansion, Scurrble Champions score 2 victory points for every other Scurrble Champion in your city and all share the same space, making it an obvious strategy to place as many of them as you can.
As the achievement says, simply place three Scurble champions and the associated building, the Scurrble Stadium in your city. Scurrble Champions placed in the Dungeon still count towards the achievement.
The "Extra! Extra! Extra!" challenge doubles the amount of Extra! Extra! cards present in the game, making this achievement much easier to complete.

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Breaking News
Achieve 3 or more events while you have a Gazette in your city.


The Gazette found in the Extra! Extra! expansion allows you to store victory points whenever you complete an event, which you then retrieve at the end of the game.
Completing three or more events with it active allows you to take an additional three victory points and unlocks this achievement.
As with the two previous achievements, you'll have an easier time getting the Gazette card when playing the "Extra! Extra! Extra!" challenge, as it doubles the amount of Extra! Extra! cards present in the game.

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Legend
Play 25 Legendary cards.


Legends adds 10 new cards to the game, with each player being given two of them at the start of the match. These are essentially upgraded versions of some of the base game cards, which can be played like normal cards or used to replace their original counterparts at no cost, expanding your city's maximum size by one along the way.
For this achievement, you have to play 25 of these cards across multiple games. As you'll only ever get two of them per game, you'll need at least 13 regular matches to unlock it.
The "Legendary Trials" challenge allows you to draw and play additional legendary cards whenever you play one, making it a good way to make fast progress with the achievement.

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Rugworts Accomplice
Play 2 or more Rugworts cards in a single game.


The Rugwort Pack introduces three new cards designed to make your opponents lifes harder. Simply draw and play any two of them over the course of a single game to get this achievement.

I hope the guide could help you to fully complete Everdell. I'd appreciate it if you'd leave a comment in case you found a mistake or poorly worded section.

Additionally, I'd be very happy if you rated this guide and/or gave it an award in case it was of help you.