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