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