Here is the full list of all 76 Cave Story+ achievements.
Obtained the Spur!
Obtained the Whimsical Star!
Obtained the Alien Medal!
Played Cave Story on April 29th!
For the rest of us!
Mask Mimiga Ending
Normal Ending
Spared Eggfish
Completed Easy Mode
Defeated the Undead Core!
Beat by Toroko
Defeated the Red Ogre!
Found and collected all Life Capsules
Obtained the Iron Bond!
Obtained Ma Pignon!
Obtained the 290 Counter!
Obtained the Tow Rope!
Obtained Curly's Panties!
Defeated Balrog!
Defeated the Muscle Doctor!
Defeated the Doctor!
Defeated Misery!
Obtained the Nemesis!
Returned Mister Little back home
Found Mister Little!
Bad Ending
Defeated the Twin Dragons!
Found and collected all Missile upgrades
Defeated Ironhead!
Defeated the Core!
Obtained the Turbocharge!
Obtained the Super Missile Launcher!
Defeated Balrog, yet again...
Defeated Puu Black!
Defeated Monster X!
Obtained the Arms Barrier!
Obtained the Blade!
Defeated Toroko...
Accumulated XX,XXX of damage
Obtained the Life Pot!
Beat Omega with Jenka's Puppy
Defeated Omega!
Obtained the Machine Gun!
Defeated Curly...
Defeated Balfrog!
Defeated Balrog, again...
Obtained the Bubbline!
Obtained Chako's Lip Stick!
Obtained the Fireball!
Obtained the Map System!
Defeated Igor!
Obtained the Missile Launcher!
Obtained the Polar Star!
Obtained the Snake!
Defeated G-Clone!
Defeated Heavy Press!
Defeated Ballos!
No Life Capsules (Good Ending)
No Life Capsules (Best Ending)
Completed Hard Mode
Completed Blood Stained Sanctuary
Completed Blood Stained Sanctuary in Less Than 3:00
Completed Blood Stained Sanctuary in Less Than 4:00
Completed Blood Stained Sanctuary in Less Than 5:00
Completed Blood Stained Sanctuary in Less Than 6:00
Completed Boss Attack
Completed Boss Attack in Less Than 8:00
Completed Boss Attack in Less Than 10:00
Completed Boss Attack in Less Than 12:00
Completed Boss Attack in Less Than 15:00
Completed Wind Fortress in Less Than 4:00
Completed Wind Fortress in Less Than 5:00
Completed Wind Fortress in Less Than 6:00
Completed Wind Fortress in Less Than 7:00
Saved Curly Brace