The best and fast way to get this achievement is by going to a personalized game with a second local player in the game to get in less than 2.10 min. But how?

• Connect a control pad or a kind of before launch the game.
  
• Go to play a custom game and select solar boss map, customize the IA's bot to low.
  
• Now just add a local player and click to ready.
  
• Pick up Scoop and Leon on your side to control both.
  
• When the game starts go with one to the shop and spend all solar possible in melee attack improvements. Do the same with the other.
  
• Now go with Scoop or Leon to the right position were Solar Boss appears. Go with the other naut you control to the same position but let theme some space between each other, just because we need the Solar Boss to get in this place when him spawns.
  
• When Solar Boss spawns and it is just between your nauts, is time to melee attack with both (press click on your mouse and the right button of you control pad for the other).
  
• Enjoy your achivement of beating in less 2.10 min the Solar Boss.

Extra info, read before comment:

Some people told me in comments other options that not require the above, but as I said this is the fast way to get, that means more fast than anyone to get the achievement. Obviously you don't need to do this to get it because you can sort with other nauts such Gnaw or Derpl, before 2:10 min, but with the above if there were a timing, you have done a best record time. So the above is the fast way to get it without being skilled.