Here is the full list of all 20 Old School RuneScape achievements. It takes around 0-1 hour to unlock all of the achievements on Windows.
Complete a Clue Scroll
Complete the Vampyre Slayer quest
Complete the Demon Slayer Quest
Equip a Mithril Scimitar
Ride the canoe in Lumbridge
Catch a Tuna at Musa Point
Visit the General Stores in Lumbridge, Falador, Varrock, Edgeville, Rimmington, Al-kharid and Karamja (Musa point)
Equip Fancy Boots or Fighting Boots from Stronghold of Security
Vote in a Poll or view Poll results
Use the Home Teleport Spell with any spellbook
Chat clothing with Thessalia in Varrock
Enter the Wilderness
Craft some Air Runes at the Air Altar
Pass through the Al-Kharid/Lumbridge gate without paying
Complete the Tutorial
Reach a total level of 100
Complete the Cook's Assistant quest
Reach Combat level 20
Visit Death's Domain
Complete the Dragon Slayer quest