The best way to get this achievement is during the first year of Career mode and immediately off the back of winning the Australian Open.
If you don't play it immediately after the previous Grand Slam: Prior to competing in the French Open you should play the minor tournament (as opposed to the training or exhibition match), to get yourself used to the gameplay. An alternative is to play a couple of exhibition matches prior to entering Career mode, so that it will not affect your attempt at the Collector achievement.
It should also be noted that at the speed these tournaments are being completed, you can complete this achievement with Australian Open Title, Wimbledon Title and US Open Title in the space of around 1.5-2 hours total.
In the first year, winning a tournament is extremely easy. Obviously, the shorter the matches, the better. A simple serve to the outside of the service square, followed by a volley to the open court will win you majority of the points on your own serve. To win on your opponents serve, simply hit it deep to the corner that your opponent is serving from. As soon as you hit the ball, you should immediately run to the net; so, when the return shot is hit, it is a simple volley into the open side of the court.
The level of play from your opponent does not increase by any noticeable level in the first year; so, you can use this tactic all the way through to win the tournament.
Using this tactic, you should also get the following achievements, if you have not won them in a previous Grand Slam:
Clean Break
Silver Set
Broke
Roland Garros Big Show
Never Broken
No Set Lost