Here is the full list of all 20 RuneScape achievements. It takes around 200 hours to unlock all of the achievements on Windows.
Completed all the tasks in the Lumbridge hard set
Crafted nature runes at the altar buried in the jungle
Unlocked the lodestone at Anachronia, the island of great beasts
Completed all the tasks in the Lumbridge Medium set
Claimed an anti-dragon shield from the Duke of Lumbridge
Solved the Embrace the Chaos mystery within the Infernal Source archaeology site
Completed all the tasks in the Lumbridge beginner set
Gained access to the golden city of Menaphos by completing the Jack of Spades quest
Climbed to the top of the white knights' castle and saw all there was to see
Unlocked the lodestone at Lumbridge, the city of stone
Unlocked the lodestone at Burthorpe, the town of training
Selected your chosen colour of kitten from Gertrude, using the ring of charos
Completed a sinkhole activity
Finished 10 clue scrolls and claimed their loot
Defeated the 6 (or 7) barrows brothers and claimed their loot 5 times over
Stepped inside the portal at clan camp and visited a clan citadel floating in the sky
Travelled to the Arc islands and visited 50 uncharted isles
Killed 1000 of RuneScape's bosses
Unlocked the lodestone at Prifdinnas, the city of the elves
Reached the highest level in a skill and unfurled a flag in the prestigious max guild garden