Campaign and Hero
These are the achievements related for the campaign and hero:
Get The Party StartedWin stage 1 with 3 stars. Win the first stage and get all 3 stars. Stage: Gray Ravens.
I Need A HeroComplete 3 stages without the hero dying. You need to have your hero alive for 3 stages in total, so play safe.
The Art Of War
Read all tip cards. You have to read every tip cards, but why will only come in the few first stages.
StargazerEarn 15 stars. In total when you reach 15 stars during the campaign you will earn it.
Only Counts As OneDefeat 10 enemies with a single thunderbolt power. Use the thunderbolt power in a single strike, and kill 10 enemies. Stage: Any.
Brave Little TailorDon't let the hero die against an Ettin on Stage 4.
Truth Or DareCall 13 or more early waves on any given stage. Befor the next wave income, press the skull 13 times in total and the next wave we come, with some extra income. Stage: Any.
Robin Of ElfwoodEarn 3 stars on each Elven Woods campaign stage. Gather all the stars from the first 6 stages, the Elven Wood and you will get it.
Not Today!Complete 7 stages without the hero dying.
Why So Serious?Defeat Hi-Hi Enha, the Gnoll Chieftain. Kill the boss Hi-Hi Enha, and you will earn it. Stage: Gryphon Point.
StardustEarn 30 stars.
Game Of ThronesDefeat Malicia!
Ace Of SpadesComplete Stage 5 without building any barracks. Don't build any barracks, during the whole stage. Stage: Royal Gardens.
Shenzi, Banzai & EdEnd stage 3 without scaring more than 3 hyenas.
PixiebellEarn 3 stars on each Faery Grove campaign stage.
We Are The ChampionsDefeat the Spider Goddess!
Great DefenderComplete the Campaign in Normal difficulty.
RockstarEarn 50 stars.
Starcraft
Earn all stars from each Campaign stage.
It's A Trap!Prevent Mactans from webbing at least 8 towers.
Red FiveComplete any stage with 5 active arcane sentinels.
City Of SplendorsEarn 3 stars on each Ancient City campaign stage.
BeorningsHave 8 or more Runed Bears in any single stage.
Heroic RushComplete all campaign Heroic challenges.
Iron RushComplete all campaign Iron challenges.
Ding! Ding! Ding!Raise all 3 basic heroes to level 10.
Background
These are achievements you get for just playing, and as you progress the story line you will have them before you'll get all the other achievements.
GnollbusterDefeat 900 gnolls. Kill 900 gnolls i total. Stage: In the first 4 stages.
FootloosePerfect Parry for a total of 1000 damage. Upgrade your Barracks to the Advanced (level 4) and buy the Bladesinger Hall, then your soldier will have the special passive ability Perfect Parry. Let them fight with you, and you will earn it. Stage: 5 and up.
Gloomicide
Defeat 100 gloomies before they duplicate.
I Volunteer As TributeDeploy 500 or more reinforcements into battle. Use the reinforcement ability, to summon some soldiers to fight for you, do this 500 times in total. Stage: Any.
Vorpal BladeDefeat 5 Bandersnatches only by dealing them damage.
The Bone Collector
Collect 100,000 gold from defeated enemies.
Jurassic Lake
Crystalize a single creep for more than 10 secs.
Gargamel
Squish 10 gnomes!
It's A Kind Of Magic
Defeat 50 enemies with Eldritch Doom explosions.
War Never ChangesHave 1,500 of your own soldiers defeated in battle.
Lullaby!Defeat 50 sleeping enemies.
1.21 Gigawatts!Cast 1210 lightning bolts.
The Bigger They Are...Defeat 7 Golems before they walk past half the stage.
D&DHave Beresad and Ashbite defeat 100 enemies.
Green ArrowDefeat 500 enemies with reinforcements' projectiles.
Tauriel ApprenticeMake 600 Blade Dance moves.
Winter Is ComingFreeze 100 enemies with the Sorcerer's Stones.
Phantom ZonedKeep enemies out of time for a total of 1000 seconds.
Heavyweight ClassStun 10 or more enemies with a single clobber.
Killer Tomatoes!Defeat 500 enemies with the poison Vines.
Counter MasterDefeat 250 enemies while silenced.
Dogfight AceHave your Gryphon Riders defeat 25 Perythons.
Kingsfoil LeavesGive regeneration 25 times to the same soldier.
Brother Vs BrotherHave your Renegades defeat 50 twilight elves.
I Meant The Red WireHave your soldiers avoid 50 blasting spell explosions.
Let the Twilight Avenger buff hes nearby enemies, with the buff called Blasting Curse. When he has done that, kill those enemies without it hit your own soldiers. To do so use your Thunderbolt ability to kill them, or a ranged hero. Stage: 7 and up.
Wildfire HarvestThrow 1,000 burning nuts.
Rambo StyleDefeat 50 flying enemies with Arcane Burst arrows.
Secrets / Click And Activate
These achievements are where you need to find and click on the specific thing/person:
ScissorfingerFind the matching bushes. Click on the three bushes and get three even. Stage: Royal Gardens.
Gathering The MagicDefeat 80 enemies with the magic Blossoms. Use the magic Blossoms and kill 80 enemies in total, as a kill (last hit). Stage: 1,2,3,4,5 and 6.
Dwarf FallsSave 13 barrelled dwarves. When you see a dwarve in the river, click on him. You need to do that 13 times. Stage: Waterfalls Trail.
George FallFind George! Click several times on the green lian, in the upper right corner, and George will swing in. Stage: Redwood Stand.
PeekabooFind the three playing friends.
Candy RushSave Hans and Ethel.
Shroom SaysComplete a 9 tap challenge of the Shroom game.
Garden SongActivate 50 magical plants. Click and use the magic Blossoms 50 times in total. Stage: 1,2,3,4,5 and 6.
White RabbitScare 11 idle white rabbits! Click on the rabbits 11 times. Stage: 1,2,3 and 5.
I Like To Move It!Entertain the funny lemure.
Killtacular!Crimson Sentence 10 enemies in a single wave.
Fee-fi-fo-fum!Grow the beanstalk to the clouds!
1,2,3...Plant!Grow 100 barbed vines!
Sorcerer's ApprenticeFind the three apprentice relics!
Valar MorghulisMark a total of 5 targets simultaneously.
Call Me Mr. PigMake the Razor Boars trample and kill 20 enemies.
No Pain, No GainDeal over 100,000 damage with Sylvan Curses.
Tower / Buildings
These are relatated for the tower and building:
SimcityBuild a Level 4 tower on every holder of a stage.
Source: https://gameplay.tips/guides/3238-kingdom-rush-origins.html