I assume you're mainly having problems with the mammoth rush right after receiving your MCV.

First, turn gamespeed down to slowest. Attempting to beat those mammoths at 60 FPS is just suicidal.

Try to form a bottleneck with your microwave tanks and light tanks. Ideally, you'll want to trap the mammoths into the valley on the eastern side of your base area; have some light tanks on the front, microwave tanks right behind them, and the artillery behind the microwave tanks. As your light tanks that are protecting the microwave tanks get killed, move in more as you receive the reinforcements.

Soviet also uses V2s to take down your Microwave tanks and light tanks from afar; for those, carefully micromanage your SSM and take out the V2s as they arrive (be careful not to get your SSM killed however, the V2s fire at it instantly if you move it close enough). If there are no V2s to fire at, use the SSM to also bombard the incoming horde of Mammoth tanks.

Eventually, if you do it well enough, the main mammoth tank and V2 rush will end (with some units still attacking every once in a while, but not in such a huge group) and you will have some units left that you can scout the map and defend your base with.

After that you've survived through the hardest part of the mission. Now it's time to just slowly expand your base, improve your economy and build up forces while defending against Soviet. Scout the map, destroy some Soviet defenses, expand to cover more tiberium fields, build more forces and eventually crush the Soviet bases one by one. (Tip: the starting elite stealth tanks are awesome for scouting as long as you don't get too close to the Soviet bases)

The mission is labeled as a Very Hard mission so it is quite a challenge, and it's also a very long mission. For me beating it took about 2½ hours IIRC (and I'm the creator of the mission), while for Bittah it took 8 hours.

If even after countless retries you're still getting killed in the mission (even with the slowest game speed), you likely aren't skilled enough for the mission yet.