It is highly recommended you have a thorough understanding of how the strategy elements and mechanics of the game work before attempting the game on Impossible. The greatest challenges you will face on Impossible difficulty is the skill and tactics of the aliens and the reduced funding/rewards you earn each month.
The following outlines the difference between each difficulty level:
Easy:
+ Initial funding of 175 credits.
+ Initial global panic level of 0
+ Monthly income increased by 50%
+ Begin with an Officer Training School already constructed.
+ Begin with 1 satellite in reserve.
+ Base begins with 35 power
Normal:
+ Initial funding of 175 credits.
+ Initial global panic of 0
+ Begin with an Officer Training School already constructed.
+ Begin with 1 satellite in reserve.
+ Base begins with 35 power
Classic:
+ Initial funding of 100 credits.
+ Initial global panic of 1 per country.
+ No Officer Training School at the beginning.
+ No extra satellites in the beginning.
+ Engineers & Scientists awarded per satellite launched is halved.
+ Base begins with 30 power.
+ Rise in panic from ignored abduction missions is 2
+ Enemies have roughly 10% greater aim/chance to score a critical
+ There are more aliens on each map compared to Normal
Impossible:
+ Initial funding of 75 credits.
+ Initial global panic of 2 per country.
+ No Officer Training School at the beginning.
+ No extra satellites in the beginning.
+ Engineers & Scientists awarded per satellite launched is halved.
+ Base begins with 30 power.
+ Rise in panic from ignored abduction missions is 3
+ Enemies have roughly 10% greater aim/chance to score a critical
+ There are more aliens on each map compared to Classic
The key to beating Impossible difficulty is taking your time and knowing the strengths and weaknesses of the aliens and how to counter them with your own soldiers and research projects. Overall there is no one way to beat the game and will depend on your own style and strategies.
Make use of the save system and be sure to have multiple save files going at once. You may find yourself saving after every 2 or 3 turns in case something goes horribly wrong or you just want to give a turn another try. It is also a good idea to make a save at the beginning of each mission (after you land on the ground, not before at the base as the missions will be random) so you can restart if you find yourself employing a strategy that is destined to fail.