Here is the full list of all 44 Islets achievements.
Complete Boss Rush
Visit the Forgotten Grave's Spirit
Reverse the Stone Witch's Curse
Visit Snoots Shop
Fall into the Deadly Pit of Recently Escaped Spirits
Open the Final Gate
Collect all 60 Upgrades
Beat a Boss With Full Health
Complete the Scavenger Hunt
Reach an Arrow Strength of 10
Defeat GutGhoul
Defeat FilthPest
Defeat BoneGolem
Upgrade your Arrow Strength
Defeat Rogue Bot
Defeat Defender Unit
Reach a Sword Strength of 10
Upgrade your Airship Again
Defeat Swamp Frog
Find both hiding spots in Rainy Plains
Defeat the Stone Witch
Upgrade your Health
Defeat the Runaway Plant
Open All 5 Paid Gates
Buy the Shrine Shifter
Collect 30 Upgrades
Buy Upgrade Markers
Defeat GrappleBot
Defeat the Forgotten Grave
Defeat MechaRat
Upgrade your Airship
Defeat the Buried Beast
Defeat the ClockMaker
Defeat the Tomb of 1000 Spirits
Collect 10 Upgrades
Defeat the Sky Pirates
Open a Post Box
Buy Map Markers
Upgrade your Sword Strength
Find a hidden nook
Defeat Grave Crawler
Collect an Upgrade
Complete Boss Rush Without Dying
Beat Boss Rush on Hard Difficulty