If you really must do this, consider taking the "super-honest and open" approach. Hence, email Company A saying
Dear Steve, unfortunately I have bad news. Thank you so much for your offer, but, believe it or not SuperCorp in Chiacgo just offered me a huge $XYZ,PQR salary to work there. As you know Steve I genuinely wanted to work for ACorp and I far prefer ACorp to SuperCorp! However as you can imagine it's not possible for me to turn down $XYZ,PQR at this stage in my career and life! I just wanted to thank you again so much for the amazing chance to be considered by ACorp! Kindly, etc.
In the incredibly unlikely chance that ACorp will make an even higher offer, they have the info. As everyone has said, it's incredibly unlikely you will get yet-another offer.
I would say,
If relevant, these are tech fields and this is my first job out of college
Don't worry too much, as it is unlikely that anyone will hate on you over this; people understand someone starting their career. Maybe in the future you can swing back to ACorp. You won't be burning any bridges if you take the "super honest, Gomer Pyle" approach to letting them know.
And by the way
(1) Obviously absolutely wrap up and secure the job at SuperCorp so it is completely, totally locked in
(2) After (1), let ACorp know promptly.