Here is the full list of all 76 Cave Story+ achievements.
Completed Blood Stained Sanctuary in Less Than 3:00
No Life Capsules (Best Ending)
Played Cave Story on April 29th!
For the rest of us!
No Life Capsules (Good Ending)
Completed Wind Fortress in Less Than 4:00
Completed Hard Mode
Beat Omega with Jenka's Puppy
Obtained the Whimsical Star!
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
Obtained the Alien Medal!
Obtained the Snake!
Mask Mimiga Ending
Spared Eggfish
Completed Easy Mode
Found and collected all Life Capsules
Obtained the Nemesis!
Returned Mister Little back home
Found Mister Little!
Obtained the Arms Barrier!
Obtained the Turbocharge!
Obtained Curly's Panties!
Obtained the Machine Gun!
Beat by Toroko
Completed Blood Stained Sanctuary in Less Than 6:00
Completed Wind Fortress in Less Than 5:00
Completed Boss Attack in Less Than 10:00
Completed Boss Attack in Less Than 12:00
Obtained the Bubbline!
Completed Boss Attack in Less Than 15:00
Completed Wind Fortress in Less Than 6:00
Completed Wind Fortress in Less Than 7:00
Defeated G-Clone!
Completed Blood Stained Sanctuary
Completed Boss Attack
Defeated Ballos!
Defeated Heavy Press!
Saved Curly Brace
Normal Ending
Defeated the Undead Core!
Defeated the Muscle Doctor!
Defeated the Doctor!
Defeated Misery!
Accumulated XX,XXX of damage
Defeated the Red Ogre!
Obtained the Iron Bond!
Obtained Ma Pignon!
Obtained the 290 Counter!
Bad Ending
Defeated the Twin Dragons!
Found and collected all Missile upgrades
Obtained the Spur!
Defeated Ironhead!
Obtained the Tow Rope!
Defeated the Core!
Obtained the Super Missile Launcher!
Defeated Balrog, yet again...
Defeated Monster X!
Defeated Puu Black!
Obtained the Blade!
Defeated Toroko...
Obtained the Life Pot!
Defeated Omega!
Defeated Curly...
Defeated Balfrog!
Defeated Balrog, again...
Obtained Chako's Lip Stick!
Obtained the Fireball!
Defeated Igor!
Obtained the Missile Launcher!
Obtained the Map System!
Defeated Balrog!
Obtained the Polar Star!