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