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