Most people that play this game will almost always end up winning the stanley cup or coming close to winning it during their dynasty seasons. This will mean your draft picks are useless because you'll be picking the garbage that the others have left behind. So with your picks useless you should make use of them by trading them for better players. To start the process take some of your crappy players(under 70 overall) and trade them up for players one or two overall points above them(the CPU will almost always accept). Sometimes when you get to a point where you need to trade that 79 overall player for a 80 the CPU will not accept and then at this point the draft pick becomes of use, now the CPU will accept 80% of those trades depending on the pick number.
To get the victory and score a goal acheivement on the different difficulties you will need to do very one not just the superstar one. The easiest way to finish these acheivements are to play a friend and make him/her be goalie. Just tell him to move aside from the net and you will score in no time this can also work for the 5 goals in one game with a player acheivement.