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UPDATE: I stayed up all night and finished the remainder of the trophies so that means this is a COMPLETE SAVE SET!! Hope you guys enjoy!
SPECIAL THANKS TO SHAHROZ47 for his Complete all challenges save, and both Streets of Rage 1 and 3 trophy saves!

The saves are for...

(READ THIS ONE!)
00 FLY YOU FOOLS! - Golden Axe 2- Kill 25 enemies by throwing/knocking them off the environment in a single play through.
Just start a new game of Golden Axe II, head right about 4 screens of enemies,
you'll then see a ledge climb up that and throw them off it into the water on the side and do the Rewind trick with L2 and keep replaying them falling,
it will pop the trophy this method (If your trophy progress in game gets stuck at 2, delete the trophy progress and try again.)

00 WHAT ARE THE BUTTONS? - Golden Axe - Use Magic when no enemies are present.
Just start a new game and press Square to use magic.

00 MULTITOOL - ALIEN SOLDIER - Use 4 different weapon modes in one session.
Just start a new game and cycle through each weapon mode until trophy pops.

00 DANCE THE ROBO - Dynamite Headdy - Defeat the Robo Collector.
Start a new game and just keep attacking the robot at the beginning, trophy pops when you beat him. (He doesn't attack.)

00 CHALLENGE ACCEPTED - Complete 1 Challenge.
Just beat Flicky or Mirror Sonic challenge, it's really easy.

00 Experience History - Play 20 games.
Just boot a game up and immediately exit and start another, once you hit 20 trophy pops.

00 It's A Lovely Day Outside - Play 50 games.
Just boot a game up and immediately exit and start another, once you hit 50 trophy pops.

01 POWER THROUGH - Space Harrier II - Earn a score of 5,000,000 points.
Load the save and the trophy pops.

02 DEMONSTRATE RESTRAINT - Shadow Dancer - Beat the first 2 stages without magic.
Load the save and walk to the exit, then trophy pops.

03 FIVE LARGE - COLUMNS - Earn 5,000 points.
Load the save and you'll earn 5k

04 500 RINGS TO RULE THEM ALL - Earn 500 rings in Sonic the Hedgehog.
Load the save and grab some of the rings until the trophy pops. (MAKE SURE YOU RESIGN BOTH SAVES FOR THIS, TROPHY PROGRESS AND MANUAL SAVE)

05 COMMITTMENT - Sonic The Hedgehog - Collect all the 6 Chaos Emeralds.
Load the save and grab the emerald, trophy pops.

06 KEEP YOUR POWDER DRY - Shinobi 3 - Get a Shinobi bonus (complete a level without throwing a shuriken.)
Load the save and the trophy pops!

07 TO THE BRIM - Golden Axe 3 - Max out your magic.
Load the save and pick up the magic on the floor with X.

08 EXTRA HEDGEHOGS - Sonic 2 - Finish Emerald Hills with 5 lives.
Load the save and head to the right to finish level, trophy pops.

09 SPIN FOR THE WIN - Sonic Spinball - Collect all 3 Chaos Emeralds in Toxic Caves.
Load the save and you'll fall directly on the emerald, trophy pops.

10 CHALLENGE X - Complete 10 Challenges.
Load the saves and do the Flicky Challenge, trophy pops upon completion.

11 GOOD JOB - Streets of Rage 3 - Finish the game on Normal or Hard difficulty. (THIS SAVE IS THANKS TO SHAHROZ47!)
Load the save and trophy pops.

12 SORE KNUCKLES - Streets of Rage - Get to the final boss without using a continue. (THIS SAVE IS THANKS TO SHAHROZ47!)
Load the save and trophy pops.

13 CLEAN SWEEP - Complete all challenges. (THIS SAVE IS THANKS TO SHAHROZ47!)
Load the save and do the Flicky challenge, trophy pops upon completion.

14 ONE IN THREE - Alex Kidd - Win 50 Games of Rock, Paper, Scissors.
Resign both the trophy progress and Alex Kidd save, Load the Alex Kidd save and win the last game of Paper, Rock, Scissors. Trophy pops.

15 ALL THE MAGICS - Golden Axe Games - Collect 200 magic.
Resign both trophy progress and Golden Axe III save, when you load in pick up the Magic with X. Trophy pops!

16 CHILLIN' OUT MAXIN' - Toejam And Earl - Dance the Hula.
Load the save and to your left is a Hula girl go up to her and press Square, trophy pops.

17 RELAXIN' ALL COOL - Toejam And Earl - Find the Secret Island.
Load the save there will be a ledge in front of you, walk of the ledge (Into the black hole) and you'll land in the secret Island, trophy pops!

18 THE EAGLE HAS LANDED - Shining Force - Make it to Alterone.
Load the save and head to the castle to the right, trophy pops upon entering.

These saves were made on the Digital US Version of the game.
Cheers!
I also have the instructions in the download itself although most don't need instructions since a lot of the saves are basically load the game, then trophy pops. Challenges require to do Flicky which is a very
easy challenge. If you need the do 1 Challenge trophy I recommend doing Flicky or Sonic as they're both really easy.