How to increase sensitivity of Light Dependent Resistor (LDR)
My question is how to increase the sensitivity of this sensor

You can't.  The response of the sensor itself is what it is.  You would have to modify the sensor to change that.

You can, however, amplify the output of the sensor.

so that it is able to measure the change of resistance within 200ms?

Now you are asking about response time.  That is completely independent of sensitivity.  Amplifying the output of the sensor will at best not increase the response time in a meaningful way.

You are using a CdS light-dependent resistor.  Those have good sensitivity, but are quite slow.  Depending on the low and high light levels, it might be possible to get a response in 200 ms.  For example, if the change in light is essentially dark to direct sunlight, then it should be possible to detect that in much less than 200 ms.  If you are looking for subtle changes, especially with both levels being quite dim, 200 ms may not be achievable.  You'll have to experiment to see what you can do.