This achievement is easiest to get if you play as a Muay Thai/Brazilian Jiu Jitsu fighter. First I trained up Clinch Grapple Offense, Ground Striking Offense and Clinch Striking Offense. At level 2 Muay Thai I would get KO of the Night in most fights using Clinch Knees (RB + Right Stick towards opponent to gain clinch, when in clinch drag the opponents head down by pulling Right stick down and hit B when their head is as low as it can go).
After fully upgrading Muay Thai, go to the BJJ camps and upgrade, and keep sparring to increase takedown offense and Submission offense. When Sub offense is at least 70 you can start going for submissions in fights. (NOTE: You CAN strike your opponents and still get Submission of the Night) Sub of the Night is easier to get if you string a counter (right stick up when opponent strikes), to a drop (RB + Right stick away from opponent in Double Underhooks defense/offense grapple), then when they punch at you, hit RB + click right stick to catch their strike and then tap X and Y as fast as possible to submit them.
When choosing an opponent for your next fight, keep in mind Wrestlers are usually easier to submit then other BJJ fighters.
Finally for fight of the night, you should get some of these awards whilst you get the sub of the night awards (I didn't get one all career until my last 7 fights when I got 7 Fight of the Nights and 7 Sub of the Nights).
If you have any questions ask me ;)