There are 3 achievements you'll be getting even if you try to avoid all other achievements throughout the game, which are:

Start
"complete first level"
Beat the first level of the game, as simple as that.


Size doesn't matter
"win battle against 4 enemies"
You'll be getting this one either at the last level of the game were you have to fight against two full enemy teams or while clearing some of the secret levels.

Hero savior
"save the princess"
Beat the game and save the princess.

These achievements are those you'll get by wearing and collecting clothes throughout the game, excluding "teams" related achievements.

Preparation
"dress any full set"
Just as the description said, wear any full set of clothes.


On the style
"dress the whole team"
Wear all four cats in full sets of clothes.


Trandy
"collect 200 a clothes"
Collect 200 individual pieces of clothing. You'll most likely be getting this one near the end of your playthrough.

Collector
"collect all clothes"
I personally got this achievement before actually getting all clothes in the game, so if i had to guess i'd say this is tied to a number of clothes rather than the actual maximum amount of clothes the game has to offer. Still pretty simple and straightforward, just collect all clothes in the game.

Achievements related to the Teams mechanic the game has where you'll unlock a bonus by discovering hidden combinations of clothes. This section also covers Artifacts and Secret Levels.

My first team
"find one the team"
Find one of the teams. You should get this by accident during your playthrough.


I know everyone
"find all the teams"
Please refer to Wordcraft's guide StrikeForce Kitty on 100% [PL/ENG] {All Teams} {Artifacts} {secrets}, it shows all 105 teams in great detail.

While going for this one you'll also get the following:

• Cinephile
  "find all the movie teams"
  
  
  
• A connoisseur of cartoons
  "find all the cartoons teams"
  
  
  
• Player
  "find all the games teams"
  
  
  
• Otaku
  "find all the anime teams"
  
  
  
• Fan of comics
  "find all the comics teams

You cannot hide from me
"defeat all secret bosses"
Secret bosses are found at the end of every secret level, and defeating them will reward you with their clothes. To find these secret levels you have to wear a certain combination of clothes to get a certain team, and then you'll have to return to the map (with the clothes equipped) so you can play the through the secret level. These levels range from A to J and the teams necessary for each level are all covered in Wordcraft's guide


Found!
"dress an artifact"
Equip an artifact for the first time.


Archaeologist
"find all the artifacts"
Simply collect all artifacts in the game.


Expert of History
"dress the all artifacts"
After getting all the artifacts, simply pair them with their respective clothes. All combinations are present in Wordcraft's guide

Achievements that come from getting 100% completion on all 20 levels and bosses.

Researcher
"complete any level to 100%"
Pretty straightforward, just full clear any level.


Liquidation
"complete all levels to 100%"
Just get all clothes and chests on each level. Doesn't include boss or secret levels.


Total destruction
"defeat all big bosses"
For a boss to count as "defeated" you have to beat it 4 times, each being a stronger version of the previous one. Simply defeat all five bosses in the game and this should be done.
While going for this achievement you'll also get the following:

• Princess in another castle
  "defeat boss 1"
  
  
  
• Grahaaa!
  "defeat boss 2"
  
  
  
• Get the cake
  "defeat boss 3"
  
  
  
• Escape from Kotaushenko
  "defeat boss 4"
  
  
  
• Forward the mighty kittens!
  "defeat boss 5"

Leftover achievements basically.

Skillful fighter
"employ every skills"
There's a total of 12 skills you can use during the game, so this should come naturally to you as you play. If it doesn't, just cicle them on your team and use them agains't enemies and it should pop in about 3 levels.


Delicious
"collect 50,000 fishes"
This'll normally pop before you even finish the game unless you manage to get through everything really underleveled.


Rich!
"get 10,000 coins"
You'll finish the game with about 7k coins if you did the "Liquidation" Achievement and also the secret levels, so you'll probably have to grind a little. While farming for coins i found it that the easiest map to do so was secret level F, which i managed to get around 40-50 coins consistenly by the end of the level.
Another thing to note is that this achievement considers the total amount ever, not the total amount you posses, so just gamble it all away if you want.


Passion
"lose 100 coins in casino"
Land on the "cat" icon while gambling at the casino.


Gourmet
"taste all the food"
Simply buy all the food at the restaurant at least once.

Thanks for reading! I've made this guide because everytime i needed any kind of info about the achievements i had to either get out of my way and dig through the minimal amount of content on youtube or translate the russian guides here on the community, so if there's anything i can improve on or any mistakes i might've done just let me know and i'll work on it.