This was probably the most difficult mission I have played so far, and I've reloaded the scenario a few times before I figured out an acceptable course of action.
My first instincts were to stick to the right side of the map, because I figured battling in close quarters would yield better results. I was wrong. My troops were dreadfully ineffective at spotting the Russian armor hidden in the forests and got torn to pieces. Also, most attempts at spotting with forward observers were met with the precise and timely artillery barrages you described. Additionally, my own artillery barrages were ineffective at softening up the enemy, and since the right hand side featured two lines of defense this turned out to be a no-go.
I tried a different approach. The left hand side was quite open, and using the high ground forest that you deploy in, I could sneak up observers to peak "around the corner" and spot the enemy armor that seemed to be waiting to counter attack. I also decided to keep all of my infantry inside their vehicles. My opening moves were to get said observers into position and use smoke to get a platoon of infantry to the left hand stretch of forest. This platoon slowly made its way through said stretch of forest while my observers got as much information on the position of the enemy armor as possible. As long as my observers moved carefully and slowly, I could ensure they did not get spotted. From here, I started calling in precision artillery strikes on every enemy vehicle I could spot. When I had sufficient intelligence, I had all my Mi-24s attack the concentration of enemy armor on the left.
While this was going on, the majority of my forces moved up the road. I positioned some tanks on the left side of the main road, overlooking the open field, because I was still anticipating a Russian armored counter attack. These tanks started spotting enemy armor in the left hand stretch of forest (also had pre-mission intelligence of at least one armored vehicle in that forest). My infantry and their vehicles were slowly moving up through said forest and clearing out the infantry positions there. The infantry together with the tanks on the main road cleared out this forest. On several occasions the infantry in the forest was being subjected to artillery barrages, at which point I simply mounted them up and patiently waited for it to end, or simply moved out of the danger area.
With the enemy armor on the left being decimated, and my infantry having cleared the left hand stretch of forest, I felt confident to start advancing on the first objective. Simultaneously I started pouring in my main force (lead by the tanks) from the main road into the field, close to the forested defensive line. From this point onward, with the enemy armor on the left mostly taken care of, resistance was surprisingly light, and the left had become a gaping hole in the enemy defensive line where I could funnel my troops in and undermine the rest of his defenses.There was a lot of infantry, but I used an unnecessary amount of firepower on anything that moved.
It should be said that it took me about one hour to one and a half hour to accomplish this. In the mean time my troops were subjected to many artillery barrages, but these weren't very effective due to all my infantry being mounted. My vehicles could reposition quickly and safely on the road, and that's what I did any time my troops got targeted. Furthermore, enemy air support was mostly suppressed by my anti-air, but the way air power works in CMBS, it's a coin toss.
In the end, I got tired of slogging through the enemy defenses and I ended the scenario prematurely with a cease-fire and ended with a minor victory.
To summarize, the main threat on the left was the armor hidden in the left hand forest, and the armor hidden in the left back corner. After that was dealt with, the door was wide open. I hope this helps.