Here is the full list of all 76 Cave Story+ achievements.
Obtained Curly's Panties!
Obtained the Machine Gun!
Completed Wind Fortress in Less Than 5:00
Completed Wind Fortress in Less Than 6:00
Completed Wind Fortress in Less Than 7:00
Defeated G-Clone!
For the rest of us!
Defeated Ballos!
Defeated Heavy Press!
Saved Curly Brace
Found and collected all Life Capsules
Normal Ending
Defeated the Undead Core!
Defeated the Muscle Doctor!
Defeated the Doctor!
Defeated Misery!
Obtained the Iron Bond!
Obtained Ma Pignon!
Defeated the Red Ogre!
Defeated the Twin Dragons!
Found and collected all Missile upgrades
Obtained the Spur!
Defeated Ironhead!
Defeated the Core!
Obtained the Tow Rope!
Accumulated XX,XXX of damage
Obtained the Super Missile Launcher!
Defeated Balrog, yet again...
Defeated Monster X!
Obtained the Snake!
Obtained the Blade!
Defeated Toroko...
Obtained the Life Pot!
Defeated Omega!
Defeated Curly...
Obtained the Bubbline!
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 Nemesis!
Obtained Chako's Lip Stick!
Obtained the Whimsical Star!
Obtained the Arms Barrier!
Obtained the Alien Medal!
Obtained the 290 Counter!
Obtained the Turbocharge!
Found Mister Little!
Defeated Puu Black!
Bad 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
Played Cave Story on April 29th!
Spared Eggfish
Beat Omega with Jenka's Puppy
Returned Mister Little back home
Beat by Toroko