This achievement can be somewhat of a chore. The best suggestion is to put the odds in your favor.
First of all there is nothing in the achievement description about the difficulty you need to play on - therefore either put it on easy or make some custom settings once you are in the game.
Secondly, you could go from the main menu to rosters, and edit a player from the team you want to use. Increase his hitting stats, and more importantly in my opinion, his speed stats, making it easier to get that illusive triple.
It's even easier if you increase the stats of every player on your team, which makes it less likely that you will create an our, making it easier to "bat around" the lineup, and you don't have to be as selective about who gets the cycle.
It's even easier if you make the team you are playing against relatively bad. Choose all their starting and relief pitchers and modify their stats - that being said, actually increase their stamina rating so that you aren't watching them being subbed out every three pitches.
Also you don't want to decrease accuracy too much (or whatever the actual stat is called), or else it's too hard to get a pitch in the strike zone, making it hard to get a good pitch to actually hit well.
Then go into an exhibition game. If possible you want to play in a stadium that is "hitting friendly". The Phillies park is good for this, as is Miller Park (Brewers), quite a few others if you know baseball. Bad parks include the Giants stadium and the Athletics stadium.