02 cavalier rough shift into 2nd gear

i recently bought an 02 cavalier from a friend and the transmission kicks real hard into 2nd gear when accelerating at moderate speed all other gears are relatively soft for the most part my friend had the motor replaced not too long before i received the car just wondering if there was any possible solutions to avoid having the tranny replaced

Well let's just start off with the basics as to what engine size and what tranny type you have.