You NEED to be on the Penalty Kill line. Your team is down one man against the opposing team for at most 2 minutes. Your AI teammates will usually try to clear the puck into your opponents side of the ice, but if you press quick enough, then your AI teammates will pass you the puck. Now, all you NEED to do is score, and if you have the game settings in your favor as suggested in the road map, then scoring will be no problem. Trophy unlocks after the 14th short handed goal is scored.
Credit to Stephleref for the idea of using Classic settings for a NEW BAP and simulating/intervening in games to get shorthanded goals.
You can also create a NEW BAP just for this trophy, but change the BAP settings to CLASSIC and time limit to 20 minute periods. Have your BAP be a RW sniper and select a team like the Montreal Canadians. Adjust the sliders in your favor as suggested in the roadmap and play the first preseason game. Score at least 4 goals and quit the game. Simulate the rest of the preseason. You will get told by the GM you have made the 3rd line. Before the first game view the NHL lines for your team. Scroll with to Penalty Kill (PK) lines, and see if you have made the Penalty Kill line (about 50% of the time you will land on the PK line). DO NOT play any games, instead SIM each game, and press to intervene when your team is on a PK. Score a shorthanded goal and quit. Rinse and repeat 13 more times, and the trophy will unlock right after your 14 shorthanded goal.