Handling and wind noise are the main problems in this kind of situation.
Directional mics are very prone to handling noise because of the relatively floppy way
the diaphragm is suspended. The solution is either to switch to an omnidirectional mic,
which has a much stiffer diaphragm mounting arrangement, or to invest in a good quality
shock mount system. Rycote are the industry leaders in this respect.
issue is wind noise, and again, Rycote are the experts. You need to move the turbulent air
as far away from the mic diaphragm as possible, as that means protecting the mic within an
envelope of still air, which is why location sound recordists on film and TV shoots, use
the 'blimps' around the mics, often with long-haired 'windjammers' to help take the energy
out of disturbed air flows.
High-pass filtering the mic will obviously help to
reduce some of the unwanted LF, but often the handling noise and wind turblence either
cause the diaphragm to bottom out, or it generates so much LF content that the mic preamps
overload or saturate, which damages the recording in a way that can't be fixed properly
Technical Editor, Sound On Sound