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