I did this in
Battle Circuit using Timed Challenge mode.
You can die and continue as much as you want, just press

to add "credits" and

to continue.
Without doing anything special*, I
played through the game in just over 34 minutes and earned 296,100 CASPO which was more than enough to pop all 3 achievements related to this.

The Great Job! achievement in Capcom Arcade Stadium worth 252 pointsIn one play session, gain 25,000 CASPO while playing Score Challenge or Timed Challenge mode.Battle Circuit is a beat 'em up
(aka 'brawler') available in the 3rd DLC pack:
Capcom Arcade Stadium Pack 3: Arcade Evolution (’92 – ’01)Battle Circuit tips: use the character
Cyber Blue, you can increase damage output by jumping and pressing

**, hold down

to combo attacks as well as
speed through dialog, save up 400 coins and buy the max HP upgrade ASAP, followed by whatever else you want except don't waste the 1000 coins on "extend".
* apparently you gain more points/CASPO if you don't Rewind (

) at all
** if you get bored of just using Blue, then Alien Green and Pink Ostrich also work well -- Green can use his special to heal, and Pink's "deathblow" special increases critical hit chance; all of the characters activate their special ability the same way, jump +

(or alternatively you can jump and press

+

)
If you own DLC pack 2, I have read that you can play through
Captain Commando in Timed Challenge mode in about 32 minutes and score more than 50,000 CASPO as well, grabbing all 3 related achievements in one go.