Just managed to win this mission.
SPOILERS follow.

The main idea was to destroy the cruisers at the first opportunity. After I deployed the units at HQ, the AI moved the upper cruiser so that it touched the ground units right at the entrance of HQ, so that in the next move I could attack and destroy it with 3 ground and 3 air units. In the next moves we changed turns surrounding and destroying the air units, but, since it happened by HQ, I had the advantage of using my air defence, so that my helicopters survived. At the very start I moved my power boat to the side of the board, beside the carrier, shooting at boats from afar in my turns. It was a good move because it engaged the enemy's bomber and 3 boats for several moves at the side of the board, and he had quite hard time destroying my boat, suffering considerable losses. My artillery I left unmoved for the crucial part of the game, gathering experience by killing any approaching units (some luck was involved in killing the first one, because in earlier attempts it managed to reach the artillery and inflict some damage to it before the Gladiators could defend it). I moved the convoy so that it would make a bridge between the HQ and factory parts of the map, and moved recon units to defend the factory neighbourhood. It turned out important when some turns later the second enemy's carrier attacked it. I used artillery, both recon squads, repaired and experienced helicopter and tank platoon to destroy the carrier. The right-lower corner tank managed to survive (gathering experience) until reaching half-abandoned enemy HQ and prevented him from healing his two remaining air units which he tried to do due to the losses they had suffered (in my earlier attempts enemy's bomber suffered less damage, and moved to destroy my artillery instead after what I was unable to destroy the cruiser which killed my units one by one). At that poimt the enemy's game was essentially lost. I attached some screenshots from save points to illustrate.