IMPORTANT: You MUST use the fighter you started out with! If you choose Axel, get killed and continue the level with Max, Blaze or Skate you WILL NOT get the achievement. If you choose Axel, you must stick with Axel and defeat Jet with Axel.
Of course, after selecting "Single Player" and "New Game", change the "Game Settings" from Normal to Hardcore. Since you will be playing on Hardcore, this means you will have 1 continue and the difficulty will be set to "Hard". This is good reason for you to make liberal use of the instant save feature. Save often - after every stage, boss, GO! checkpoint or enemy. However necessary you find it depending on your personal skill level.
Reach the end of Stage 2 to face Jet who is, appropriately enough, flying around via jetpack. You will also be bombarded with a crowd of bald thugs mostly named Donovan that appear to be there for a Vin Diesel look-alike contest... and to beat your ass. Use the classic beat 'em up trick known as the "Zig-Zag Technique" (see my Golden Axe "Perfect Win" guide in my soultions in the link below) to take out these baldies.
My Solutions: https://www.trueachievements.com/solutions.aspx?gamerid=8453...Eventually they'll stop spawning and you'll be left mano y mano with Jet. Jumpkicking him works not only to hit him as he hovers, but as a way to rack up easy points for the "800,000 pts. on Hardcore settings" achievement. Time your jumpkicks and he'll eventually go down. If he kills you, reload your save and try again.