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