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