The King of Fighters XIII

Best done in Versus mode, two controllers required.

Notation notes:
D=Down
DF=Down/Forward
F=Forward
LP=Light Punch
HP=Heavy Punch
LK=Light Kick
HK=Heavy Kick

A Max Cancel is HyperDrive Mode Super Cancel into Neo Max Special move.

Start Versus Mode, select a 1vs1 match.
Select your characters, and a group of options will appear before the match starts, letting you alter the settings.
For Player 1, or your Gamertag character, select the option:
Level 5 P HD MAX. This will start you with a full HyperDrive gauge and 5 meter stocks.
For Player 2, the dummy character, select the option:
Level 1 HP 50%. This will start your opponent at half vitality.

I'll use Terry Bogard as the example character, as his Max Cancel is fairly easy to execute.

When you first start, move over to your opponent and punch him twice with HP to deplete his health a bit. This will guarantee that you get a KO when you hit with the Max Cancel.

To enter HyperDrive mode, press LK+HP(Light Kick+Hard Punch). When you move, you'll see a streaming aura behind your fighter.
Once active, the HD meter will deplete quickly.

While in HD mode, use Terry's Buster Wolf Super Special Move.
The notation is D,DF,F,D,DF,F+LK or HK
If you're familiar with Street Fighter, that's two fireball motions

Once the first hit of Buster Wolf connects, quickly input:
D,DF,F,D,DF,F + LP and HP simultaneously to execute Terry's Trinity Geyser, which is Terry's Neo Max Super Special Move.
You should cancel the second hit of the Buster Wolf into Trinity Geyser if done right, and MAX CANCEL will appear on the screen.
Repeat 50 times, one the 1v1 setting this will maybe take an hour

Additional notes:
Choose 1v1 because it's easier to start with a full gauge for the 1st round and an easy KO for the second round. You can do this 3v3, but it involves a lot of meter building after the first round.

Performing the MAX Cancel will also stack towards these two achievements, as you're using the Neo Max SSMs
Hey!-Hit with 100 Neo Max Super Special Moves
And the Final Blow.....-Perform 50 Neo Max Super Special Move finishes.

Okay!