To unlock the character related achievements, you just need to be in the battle, you can be idle.
If you have more than 1 controller attached, set them all to human and each controller counts as a participation, meaning as few as 5 battles are actually needed.
If all 4 are idle, you can set the rules to any timed mode and just twiddle your thumbs for 3 minutes.
Some characters need to be unlocked via story mode first.