How to minimize the heat loss in a chemical reaction

The usual answer (and correct) is to improve on the insulation, for example by covering the calorimeter, and using two cups, one inside the other.

Further improvements can be made
1) carrying out the experiment over as short a period of time as possible. reason; any calorimeter will loose heat, but the shorter the time allowed, the less heat will be lost.
2) Use a larger calorimeter, with greater volume of solution. reason; the greater the solvent mass requires more energy to obtain the same change in temperature. You get a smaller temp change for the same reaction, so less losses to the surroundings.
3) calibrate your calorimeter heat the same volume of pure water to a similar temperature as that which the reaction produces. Then determine the rate of heat loss over a period of time, say take temp every minute for 30 minutes, and plot a graph. This will give you a calibration curve that you can use to apply a correction for your calorimeter.