I know this game has been around for a while, and doesn't have a huge following, but after seeing the other solution, I felt I had another solution that works just as well, if not better. For those who still play, I think this approach will help "version up" (this game's way of "leveling up"), and help you blow through the Story mode on a harder difficulty to get those achievements too. Here goes:
1) Go into MULTIPLAYER
2) Go to CREATE MATCH
3) Go to GAME MODE SETUP
4) Set MATCH TYPE to PRIVATE MATCH
5) Set GAME MODE to DISINTEGRATION
6) Set MAPS to one of the following: HEAT SINK, HARD DISK, SPIRES, or SKYLINE (the last 2 are DLC, and all 4 maps do not allow Light Cycles. If a map allows Light Cycles you can't play against NPCs/Bots)
7) Set MAX PLAYERS to 10
8) Set TIME LIMIT to whatever you like based on what you set SCORE LIMIT to in #9
9) Set SCORE LIMIT to whatever you like in terms of how many derezzes (kills) you want to get
10) Hit Y to start the match.
11) Press left on the D-pad to activate the Heavy Disc. Only use the Y button for your attacks. Remember this is a special disc power you will need to recharge this often. You must get the derezz of the enemy using Y.
I have found this method quickest to the 50 derezzes, as well as a way to version up rather quickly, gaining those MB to perform SYSTEM UPGRADES quicker (thus unlocking the achievements related to these quicker as well). In addition, by versioning up and upgrading while doing MULTIPLAYER, your version and upgrades will carryover into the STORY mode, thus allowing you to go through the story on a higher difficulty to get the story-related, and difficulty-related achievements easier.
The above method can also be used for the achievements related to the other disc mods (Bomb, Stasis, and Corruption) as well. You can do all this in a PUBLIC MATCH too against other players, that is of course if you can find one (lately there seem to be a few people on playing which is more fun than just bot bashing). Just remember, left on the D-pad and Y are the keys here.