The Stanley Cup is awarded to the team that wins the playoffs at the end of the season. You must do this 3 times in a row for this achievement.
Before entering franchise mode, make sure the difficulty is set to Pro.
Strategy 1:
Choose a good team and simulate each year, making sure you make the playoffs. Once you get to the playoffs, save. Then sim each series, one at a time, making sure you win each one. After you win a series, save. If you ever lose a series, reload your last save. Repeat 3 times.
Strategy 2:
Edit a team's stats so that all of the players are amazing. Go into franchise and simulate the season. Once in the playoffs, use the save/reload technique (see step 1). Repeat 3 times.
Strategy 3:
Change player sliders (like step 2) and change the in-game sliders in your favor. Play each game. Once in the playoffs, win every series until you win the Stanley Cup. Repeat 3 times.