These are story related and can't be missed

Top of the class!
Completed basic robot training.

First time outdoors
Venture out of the mansion.

Fire and rescue
Rescue the family from the burning house.

Do Androids dream?
Of dead Old Men?

Ginger Tom
Return the blind man's cat.

Neat and Tidy
Use the Atlas Gloves to tidy up the village hall.

Killing Machine
Defeat the K-Bot 100 Boss.

Lots of small problems
Defeat the Nanobot Boss.

Percussionist
Learn to play the drums.

Prison break
Spring Logan from prison.

Family Reunion
Reunite with Heather and the Old Lady.

Clear the Decks
Kidnap Mr. Deck from the TV Studio.

Life is a state of mind
Go on a most excellent adventure with the Professor.

Wonderland!
Meet up with Alice and Sim.

Gardening time
Defeat the Earth boss.

Blowing in the wind
Defeat the Air boss.

Water way to go
Defeat the Water boss.

Flame off!
Defeat the Fire boss.

Brain storming
Defeat the Ether boss.

Out of this world
Travel to the secret moon base.

I am the champion
Win The One Tournament.

Bell 222
Defeat the helicopter boss.

Mercy, merci
Save the Man in Black.

Trial by fire
Don't save the Man in Black.

Looks like this achievement glitches if you don't save him, so that you get both "Mercy, merci" and "Trial by fire", but it you do save him you only get "Mercy, merci".

Game over
Complete the game.

Mission complete
Reach the end of the game having cleaned one million things.

This achievement requires you to collect 1'000'000 junk and then finish the game. The game has a lot more junk than 1'000'000, so you can leave a lot of junk behind you without worrying too much. You can get this achievement even after finishing the game once, just load your save and you're good to go.
EXTRA TIP
If you take a picture in the photo booths with the correct hat, it will give you extra junk.

Spider-robot
Climb walls with the Shoees for the first time.

Unmissable, it's story-related.

Cleaning Virgin
Clean up your first thing.

Unmissable, it's story-related.

Cleaning Beginner
Clean 1000 things.

Cleaning Master
Clean 10000 things.

Cleaning Professional
Clean 100000 things.

You will get these three achievements normally playing the game.

Cleaning Wizard
Clean 1000000 things.

To get this achievement you need to collect 1'000'000 junk. Easier than it looks, the game has a lot more to collect (around 1'250'000). Keep an eye for secret rooms, they're full of junk.

This is the age
Take your first train ride.

A ton
Earn £100 from jobs, junk yards and other winnings.

Bag of sand
Earn £1000 from jobs, junk yards and other winnings.

These three achievements are unmissable, you'll need £1000 for a train ticket, and you'll need to work to get them.

Loaded
Earn £10000 from jobs, junk yards and other winnings.

You can easily get this money when the junkyard will open, or just grind some jobs, you'll get around £1000 per job at tier 3.

Weary of life
Die 1000 times.

Pretty easy, you'll die a lot in the game, I personally got this without trying.

Postie
Help to sort the post.

Alreet, pet!
Help to make bricks.

Dry spell
Help to wash dishes.

To get these three achievements, just do one of these jobs at least once.

Cor-blimey trousers
Empty 10 bins.

Just throw away the bins you find in the world and you'll get this.

Unbuttered fingers
Catch 200 objects.

This one is pretty easy, just pick every item you can pick and you'll eventually get it.

Consumer
Buy an item from a shop.

Shopaholic
Buy all possible shop items.

Self-explanatory, buy one item/upgrade in the shop and you'll get "Consumer", buy all items/upgrades from all the shops and you'll get "Shopaholic".

Lick of paint
Find an alternate title screen skin.

Gallons of paint
Find all the alternate title screen skins.

Scattered around the game map, there are letters which form the word "HORACE". Collect one to get "Lick of paint" and collect them all to get "Gallons of paint".

Cartographer
Complete the auto map by visiting every room in the mansion.

You will get this achievement when you complete the map of the Mansion. If you don't get it immediately, don't worry, I got it when I found a random secret room.

It's a secret!
Find a secret room in the mansion.

Top secret!
Find all the secret rooms in the mansion.

Around the mansion, there will be doors that will not appear on the auto map. Just enter these room and you'll get a purple question mark on the map. Find one and you'll get "It's a secret", find them all and you'll get "Top secret!".

Slam dunk
Score 100 baskets in total.

This one is pretty easy, since you find a lot of baskets with basketballs during the game. Just get under the basket and throw the ball, you'll get the achievement after a while.

Trainspotter
Ride on all the trains.

This achievement is odd. It says you need to ride all the trains, but I got it while WATCHING them come and go in one station.

Insert coin
Play an arcade game.

Just play an arcade game in the Arcade and you'll get the achievement.

Games master
Get the high score on all the arcade games.

Self-explanatory, get the high-score in all the arcade games. A couple of them are only available in the "Nentindo" console in the pause menu.

Mode 7
Read 15 teletext pages.

In order to get this achievement you need to buy the tv remote from the shop, first.
Type "100" anytime in the game and you'll get the Teletext. Read 15 pages, and you'll get the achievement.

Avoid the blame
Get the kids blamed for shop lifting.

Go to the shop in Mainton and pick an item. When the shopkeeper looks away exit the shop. You'll get a cutscene and the achievement

Quack quack
Push all the rubber ducks into the water in the Laundry Room.

In the Mansion you'll find a "Laundry Room". Just push the rubber ducks in the water and you'll get the achievement.

Hacker
Run the BASIC program everybody knows and loves...

This one is tricky. Access one of the computers scattered around the map and type this:

• 10 PRINT "Hello world!"
  
• 20 GOTO 10
  
• RUN

Big thumbs up!
Complete all other achievements.

Pretty self-explanatory. Congratulations!