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