The Score Attack achievement descriptions are basically misleading and wrong. What it actually means is "We have set a high score, beat it". The high score for each fight is 4 million, with the exception of the Kid Buu 2 fight in which the high score is set to 1.5 million.
There are two strategies for this, however one is really only useful until a certain point.
Easy Difficulty Method:
This method is pretty much only useful up until Vegeta in the Saiyan Saga.
Set the difficulty to Easy. Have no QR code power-ups on (you can go into the Options menu in the Main menu to turn them off). As soon as the fight begins wail on the opponent, lean forward to make your character move closer to them if you must. If they block stop attacking and wait until they stop blocking. Eventually your Assault Gauge will fill and you will enter the quick-time event where you fill your Assault Gauge three times more. You'll want to make sure you succeed at each of these. Once that is over, take the time to fill your Ki Meter as much as possible until the opponent comes towards you and is in melee range then repeat the Assault Gauge process. Once your Ki Meter is full, hopefully your Combo Meter is at 5.0x now (if it was reset by being hit, restart the fight and try again. If you've filled your Ki Meter before your combo has reached 5.0x then just continue wailing on the opponent until is at 5.0x) then you want to immediately use your second Super Attack (that's the one at the top that uses all your Ki Meter's charge). Repeat this process a second time. This should put you over 2 million. If the opponent is not dead, finish him off however you want and win the fight. You should receive the win bonus of x2 which should bring your score to 4 million.
Normal Difficulty Method:
Set the difficulty to Normal. Use the QR code for Kid Buu if you have not yet unlocked him. The reason we use Kid Buu is that he has pretty good health (since you need survivability for this method) and other characters with A-rank attack will not leave enough room for error. You can however use someone like Super Gogeta who has A-rank health and B-rank attack for this method if you prefer but I find Kid Buu's second Super Attack to be the easiest to pull off. Before you begin make sure you don't have any QR code power-ups active (go into the Options menu in the Main menu and slide it off if given the option). One final note is that harder enemies (i.e. Perfect Cell, Kid Buu) will put up shields that make filling the Assault Gauges via melee basically useless.
Now enter the fight and attempt to build your Ki Meter (use Kid Buu's second Super Attack motion to charge it) until you're able to use the jump action (appears above the Ki Meter), however some enemies will prove to be annoying and beat the crap out of you before you can do very much. If this is the case simply try to wait until the enemy does the jump action for you and win the Assault Gauge quick-time event if you can. Once your at Ki Blast distance begin building your Ki Meter and dodging the big Ki Blasts the enemy will launch at you. Once it's full you will begin wailing on the enemy with your Ki Blast's until you get a 2.0x combo at which point you want to use your second Super Attack (if your using Kid Buu as I suggested just raise your right arm upwards). You then repeat this process. Now once you have done it a second time you might still be short of the total you need (1,333,334 points) so I suggest doing the same thing again but this time you don't need to build your Combo Meter up and if your close enough you can use your first Special Attack (which nets roughly 120,000).
Notes: If during any of the parts you do at a longer distance from the enemy (i.e Ki Blast range), the enemy decides to use the jump option to get closer to you, first win the Assault Gauge quick-time event and then you should still have the option to jump, do this as quickly as you can and win the quick-time event again and continue the process from where you got to, except with a little more of a combo now. Be careful of small red Ki Blasts these will instantly reset your Combo Meter and move rather fast, enemies normally fire them at the same time as they move so watch closely. If the enemy uses their Super Attack during any of this and you have the option, always dodge (right most option) - interrupting takes up more Ki and benefits you in no way.