Each level has 3 regular carrots and one gold carrot to collect, except for the first level which does not have a gold carrot. These are the games currency. The carrots are not hard to find so you will have no problem getting this naturally by just playing through the game.
Despite the trophies description, I did not have to buy the Power Aura for this to unlock, but if it doesn't unlock for you when you finish the level where you collected your 15th carrot then instead of choosing to move on to the next level choose the option that looks like two swords crossed behind a shield and purchase the Power Aura (cost: 7 carrots).
As a side note, golden carrots re-appear in the same place each time you replay a level so they can be used to grind for money if needed.