Here is the full list of all 86 Melvor Idle achievements. It takes around 200 hours to unlock all of the achievements on Windows.
Reach Level 99 for Ranged in Standard Mode
Reach Level 99 for Fletching in Standard Mode
Defeat Elder Wizard in the Hall of Wizards in Standard Mode
Defeat Protector of Ice in the Frozen Cove in Standard Mode
Acquire a Lemon
Defeat Aeris in the Air God Dungeon in Standard Mode
Reach Level 99 for Hitpoints in Standard Mode
Reach Level 99 for Strength in Standard Mode
Reach Level 99 for Defence in Standard Mode
Defeat Elder Dragon in the Dragons Den in Standard Mode
Acquire the Dragonfire Shield
Reach Level 99 for Attack in Standard Mode
Reach Level 99 for Thieving in Standard Mode
Reach 200 Total Bank Slots
Reach Level 99 for Runecrafting in Standard Mode
Reach Level 99 for Crafting in Standard Mode
Acquire the Fire Cape
Defeat Malcs, the Guardian of Melvor in the Volcanic Cave in Standard Mode
Defeat Prat, the Protector of Secrets in the Volcanic Cave in Standard Mode
8
Acquire the Ancient Ring of Skills
Acquire the Ancient Ring of Masteries
Reach Level 99 for Smithing in Standard Mode
Defeat Bandit Leader in the Bandit Base in Standard Mode
Reach Level 99 for Cooking in Standard Mode
(Currently Bugged) Acquire Mastery Level 99 for any item in any Skill
Acquire the Amulet of Looting
Reach Level 99 for Firemaking in Standard Mode
Reach Level 99 for Fishing in Standard Mode
Reach Level 99 for Woodcutting in Standard Mode
Reach 100 Total Bank Slots
Defeat The Kraken in the Deep Sea Ship in Standard Mode
Defeat Zombie Leader in the Undead Graveyard in Standard Mode
Defeat Spider King in the Spider Forest in Standard Mode
Defeat Mumma Chicken in the Chicken Coop in Standard Mode
Acquire the 69th Item (Based on Item ID)
Acquire Level 99 in any Skill
Reach Level 99 for Mining in Standard Mode
Find your first Pet
Create a Character
Level up any Skill for the first time
Reach Level 99 for Magic in Standard Mode
Reach Level 99 for Prayer in Standard Mode
Reach Level 99 for Slayer in Standard Mode
Reach Level 99 for Farming in Standard Mode
Reach Level 99 for Herblore in Standard Mode
Reach Maximum Skill Level in Standard Mode
Achieve 100% Item Completion
Achieve 100% Pet Completion
Achieve 100% Mastery Completion
Achieve 100% Monster Completion
Achieve 100% Completion
Defeat Glacia in the Water God Dungeon in Standard Mode
Defeat Terran in the Earth God Dungeon in Standard Mode
Defeat Ragnar in the Fire God Dungeon in Standard Mode
Acquire the Stormsnap
Acquire the Cloudburst Staff
Acquire the Earth Layered Shield
Acquire the Big ol' Ron
Acquire the Red Party Hat
Reach 80 Total Bank Slots in Hardcore Mode
Get killed by a Plant in Standard Mode
Lose your Hardcore Character by dying
Reach Level 99 for Attack in Hardcore Mode
Reach Level 99 for Strength in Hardcore Mode
Reach Level 99 for Defence in Hardcore Mode
Reach Level 99 for Hitpoints in Hardcore Mode
Defeat Mumma Chicken in the Chicken Coop in Hardcore Mode
Defeat Zombie Leader in the Undead Graveyard in Hardcore Mode
Defeat Bandit Leader in the Bandit Base in Hardcore Mode
Defeat Elder Wizard in the Hall of Wizards in Hardcore Mode
Defeat Spider King in the Spider Forest in Hardcore Mode
Defeat The Kraken in the Deep Sea Ship in Hardcore Mode
Defeat Protector of Ice in the Frozen Cove in Hardcore Mode
Defeat Elder Dragon in the Dragons Den in Hardcore Mode
Defeat Prat, the Protector of Secrets in the Volcanic Cave in Hardcore Mode
Defeat Aeris in the Air God Dungeon in Hardcore Mode
Defeat Glacia in the Water God Dungeon in Hardcore Mode
Defeat Terran in the Earth God Dungeon in Hardcore Mode
Defeat Ragnar in the Fire God Dungeon in Hardcore Mode
Defeat Malcs, the Guardian of Melvor in the Volcanic Cave in Hardcore Mode
Reach Level 99 for Range in Hardcore Mode
Reach Level 99 for Magic in Hardcore Mode
Reach Level 99 for Prayer in Hardcore Mode
Reach Level 99 for Slayer in Hardcore Mode
Reach Level 99 for Agility in any Gamemode