Here is the full list of all 76 Cave Story+ achievements.
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!
Completed Boss Attack
Completed Boss Attack in Less Than 12:00
Completed Boss Attack in Less Than 15:00
Completed Blood Stained Sanctuary in Less Than 5:00
Completed Blood Stained Sanctuary
Completed Blood Stained Sanctuary in Less Than 6:00
Defeated Ballos!
Defeated Heavy Press!
Saved Curly Brace
Defeated the Red Ogre!
Found and collected all Life Capsules
Obtained the Iron Bond!
Obtained Ma Pignon!
Returned Mister Little back home
Found Mister Little!
Obtained the 290 Counter!
Defeated the Twin Dragons!
Obtained the Tow Rope!
Obtained the Super Missile Launcher!
Beat Omega with Jenka's Puppy
Obtained Curly's Panties!
Obtained the Missile Launcher!
Normal Ending
No Life Capsules (Good Ending)
Completed Hard Mode
Defeated the Undead Core!
Defeated the Muscle Doctor!
Defeated the Doctor!
Defeated Misery!
Defeated Ironhead!
Defeated the Core!
Obtained the Turbocharge!
Defeated Balrog, yet again...
Defeated Monster X!
Obtained the Arms Barrier!
Defeated Puu Black!
Obtained the Blade!
Defeated Toroko...
Accumulated XX,XXX of damage
Obtained the Life Pot!
Defeated Omega!
Obtained the Machine Gun!
Defeated Curly...
Obtained the Bubbline!
Obtained the Map System!
Defeated Balfrog!
Defeated Balrog, again...
Obtained the Fireball!
Defeated Igor!
Defeated Balrog!
Obtained the Polar Star!
Obtained the Snake!
Obtained the Spur!
Obtained the Nemesis!
Obtained Chako's Lip Stick!
Obtained the Whimsical Star!
Obtained the Alien Medal!
Bad Ending
Mask Mimiga Ending
No Life Capsules (Best Ending)
Completed Easy Mode
Completed Blood Stained Sanctuary in Less Than 3:00
Completed Blood Stained Sanctuary in Less Than 4:00
Completed Boss Attack in Less Than 8:00
Completed Boss Attack in Less Than 10:00
Completed Wind Fortress in Less Than 4:00
Played Cave Story on April 29th!
Spared Eggfish
Found and collected all Missile upgrades
Beat by Toroko
For the rest of us!