I am confused. What am I misunderstanding?
I believe that a shutter speed of 1/25 or 1/30 would be a longer exposure than 1/160? I am a beginner so forgive me if I'm in error. But your picture is most likely sharper in this 1/160 because of the faster shutter speed - more likely it was able to stop motion of wind or camera shake. Your pictures that are at 1/25 or 1/30 may have a less sharp focus because those shutter speeds are slower and less able to stop motion / camera shake. You should be able to get sharper images at 1/25 or 1/30 with the use of a tripod - (assuming your flower isn't blowing in the wind). If you shoot slower shutter speed using a tripod you can probably also lower your ISO as you will have more light to use.
Experience - Enthusiastic Hobbyist. Equipment-Nikon D3100 & Nikon P7700, Particular Interest - Nature, Macro (mostly I needed a reason to get out of the chair, away from a computer and out of doors!)