"进入胎动期" can be translated as "entering the fetal movement period" or more naturally as "reaching the stage of fetal movement" in English.
For a more concise and commonly used expression in medical or pregnancy-related contexts, you might also hear or see "entering the quickening stage" (though "quickening" historically refers more to the mother's first perception of fetal movement, the concept is related), but strictly for "进入胎动期" (entering the period when fetal movements are regularly occurring and can be felt), "entering the fetal movement period" is accurate.
A slightly more conversational or descriptive way could be "beginning to feel regular fetal movements" or "reaching the point where fetal movements are noticeable," though these focus more on the mother's experience rather than the medical term for the period itself.
For a direct and medical translation, "entering the fetal movement period" is suitable.