After Beating Story Mode, defeating the Final Boss of Access Ark, and watching the Credits, the next you enter Story Mode, the game will show a message saying that you've unlocked the "Ability Testing Area". While Kirby is in the Access Ark Hub, go to the right of Access Ark 6-2 to enter the "Copy Ability Testing Room". The "Ability Testing Area" is an area filled with two sections that have all of the game's Copy Abilities. In the main area is a Metal Waddle Dee and some tiny Star Blocks that Kirby can use to practice his Copy Abilities. The second area there's a Robobot Armor, its Mode Abilities, some enemies, and hidden items. You can also come here to grab a particular Copy Ability, leave using the Warp Star, and keep it so that you use it for certain Stages. However, you can't take the Robobot Armor out of here.
Amiibo Powers
Every Smash Bros Amiibo (excluding third party) can give Kirby a certain copy ability. With all other third party or other Amiibo giving you a random ability. It should be noted that the Smash Bros Amiibos of Kirby characters are different than using the Kirby series Amiibo. With SSB Meta Knight and King Dedede giving you a random color change along with their power, while Kirby series Meta Knight, King Dedede, and Waddle Dee give the powers along with a color scheme matching the character. SSB Kirby gives you the Smash Ability, while Kirby series Kirby gives you UFO. This list has all the abilities granted from the Amiibo you can use. Note: Using Kirby Series Amiibo will also give you a Maxim Tomato and a random sticker each time you use them.
Ability
How to unlock
Archer
Duck Hunt, Pit, Dark Pit
Beam
R.O.B. (NES or Famicom)
Bomb
Bowser Jr, Diddy Kong, Samus
Circus
Mr. Game & Watch
Cutter
Toon Link
Doctor
Dr. Mario, Wii Fit Trainer
ESP
Ness, Lucas, Mewtwo, Shulk
Fighter
Donkey Kong, Lucario, Little Mac
Fire
Mario, Luigi, Charizard
Hammer (King Dedede Colors)
Kirby Series King Dedede
Hammer/Color Change
SSB King Dedede
Ice
Rosalina & Luma
Jet
Fox, Falco
Leaf
Villager, Olimar
Mike
Jigglypuff
Mirror
Palutena, Zelda
Ninja
Greninja, Shiek
Parasol
Peach
Parasol (Waddle Dee Colors)
Parasol Waddle Dee
Poison
Ganondorf
Smash Bros.
SSB Kirby
Spark
Pikachu, Robin
Stone
Bowser
Sword
Link, Marth, Ike, Lucina, Roy, Mii Swordfighter, Mii Gunner, Mii Brawler, Corrin
Sword (Meta Knight Colors)
Kirby Series Meta Knight
Sword/Color Change
SSB Meta Knight
UFO
Kirby Series Kirby
Wheel
Wario, Captain Falcon
Whip
Yoshi, Zero Suit Samus
Halberd on the Title Screen
Clear Story Mode and Defeat the Final Boss.
Jukebox
Clear Meta Knightmare Returns.
Meta Knightmare
Returns Clear Story Mode.
The Arena
Clear Story Mode.
The True Arena
Clear Meta Knightmare Returns and The Arena.
UFO without amiibo
Normally UFO is only available by using the Kirby series Kirby amiibo. However, after obtaining a 100% file, a UFO enemy will appear in the copy ability testing room for you to use in Story Mode. It will still be unavailable in the Arenas, however. Obtaining a 100% file entails getting all Code Cubes and beating Story Mode, clearing all stages of Kirby 3D Rumble and Team Kirby Clash, getting all stickers, clearing Meta Knightmare Returns, and clearing both Arenas.
Unlock SSB Kirby without Amiibo
To unlock SSB Kirby you have to go to level 1-4 and progress through the level until you get to the spot with 4 or 5 holes then drop in them and then fly to the left and press up.