Here is the full list of all 76 Cave Story+ achievements.
For the rest of us!
Defeated Ballos!
Defeated Heavy Press!
Mask Mimiga Ending
Spared Eggfish
Completed Easy Mode
Obtained the Whimsical Star!
Obtained the Spur!
Obtained the Snake!
Normal Ending
Saved Curly Brace
Defeated the Undead Core!
Defeated the Muscle Doctor!
Defeated the Doctor!
Defeated Misery!
Defeated the Red Ogre!
Found and collected all Life Capsules
Obtained the Iron Bond!
Obtained Ma Pignon!
Obtained the 290 Counter!
Obtained the Nemesis!
Returned Mister Little back home
Found Mister Little!
Bad Ending
Defeated the Twin Dragons!
Found and collected all Missile upgrades
Obtained the Alien Medal!
Defeated Ironhead!
Defeated the Core!
Obtained the Tow Rope!
Played Cave Story on April 29th!
Obtained the Super Missile Launcher!
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!
Obtained Curly's Panties!
Accumulated XX,XXX of damage
Obtained Chako's Lip Stick!
Beat by Toroko
Beat Omega with Jenka's Puppy
Defeated Omega!
Obtained the Machine Gun!
Defeated Curly...
Defeated Balfrog!
Obtained the Map System!
Obtained the Bubbline!
Defeated Balrog, again...
Obtained the Fireball!
Defeated Igor!
Obtained the Missile Launcher!
Defeated Balrog!
Obtained the Polar Star!
Defeated G-Clone!
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