Hitting for cycle requires a single batter to hit a single, double, triple, and home run all in the same game. This may be more difficult in manager mode where you are focusing on pitch-by-pitch or by at-bats, but can be obtained from a fully-simulated game in general manager mode.
I suggest taking control of a team from a lower division, where the talent is more widely varied. I earned this achievement in just my second game as general manager of the single-A Jupiter Hammerheads. A strong prospect against a low-quality pitcher appears to stand a better chance than a solid major leaguer against major league pitching.