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