Mac book air shuts off randommly

What year is your Mac?

Do you have any other kind of symptoms like fan at full spin, slowness, high temps, etc.

Also try

Reset SMC https://support.apple.com/en-us/HT201295

Reset NVRAM https://support.apple.com/en-us/HT204063

Restart your Mac holding Shift to load Safe Mode. It's a bit longer boot, but once it's up, reboot normally and check if it got any better.

Also check Activity Monitor to see if there is any app or service using too much CPU.

You can also try a clean install of macOS as a last attempt.

Is your Mac still under warranty? If yes and nothing of the above options solved your problem, take it to an Apple Store or Authorized Service Provider so Apple can check if something else is going wrong.

Oh, so your battery can be the source of your problem.

Don't fool around with this alert of battery service. A faulty battery can provide unstable energy and end up causing other problems in your Mac like killing the CPU or any other circuit. as you know, Macs have a logic board with everything in it and Apple doesn't repair it, they only replace the entire board, so that can cost you even more than the battery replacement.