Getting most of the battle mode achievements are pretty simple. For a lot of them the simplest way to get them is to toggle various options.

Powerup Achievements

For these achievments simply put the game on the highest time limit with all the powerups on and on frantic mode. Run around the level spamming powerups.

Gassy: Use the gas cloud 5 times
Deathwish: Pickup 5 poison
Full House: Use every type of power up in a round
Inedible: Use Invincibility 5 times
Bubble Bobble: Use the bubble power 5 times
Ice To See You: Use the slippy power 5 times
Environmental Menace: Use the sticky power 5 times
Speed Demon: Use the speed boost 5 times
Brundlechomp: Use the teleport 5 times

Five a day: Reach x5 multiplier.
Simlply turn off all items but the multiplier and put the items in frantic
Press space at the battle mode screen to go down to powerups. The multiplier is the apple. So just make sure a check mark is only beside the apple.

x5/x10/x20
Put the game on max time and turn on only invincibility stars with frantic drop. Run around from star to star and concentrate on taking out whoever your target is. As long as you keep your distance from the red and keep spamming the invincibility you should be able to get a x20 chomp combo without being chomped yourself.

Mostly Harmless:
You can either sit there and do nothing or put the game on the shortest time with no powerups and avoid everything. Avoiding everything also get you the fast food achievement.

Fast Food:
Either use the method you used for mostly harmless or you could use the method you used in the x20 chomps and just keep using invicible stars but a shorter time limit.