Hi,
first of all - hi Forum - i´m new here (but PG veteran since the first version and utterly happy about the revival of the spirit in Panzer Corps). The good and friendly spirit in the forum and the fact that i just bit may way through Cobra last weekend (Colonel difficulty on Ipad) left me no choice other than to reply to this thread.
I failed miserably in Cobra the first time i tried.
I divided up my force up in several minor battle groups to cover all the deployment clusters and tried then to frontally attack - my casualties were horrendous.
The second time lead to success when i focused my force to north east and the south west (basically avoiding the bocage center towards northwest).
East: The key to break through the eastern fortification frontally was combined arms with a focus on artillery and inf. (Especially 5* Churchill AVRE did amazing job - so did the Crocodile (i have two of them in my core and absolutely love them vs light targets)).
I hammered my way through the defensive line with arty and combined arms - progressing slowly.
For the Panthers, you need to weaken them with Tac bombers over and over again and finish them with the Firefly.
The key is, that you have time on the eastern front - you only need to capture the two eastern cities with your eastern assault group - as the southern cities will be taken coming from a small, but highly mobile force from the west.
So advance slowly, use the terrain and keep your force covered by arty as much as possible.
West: The western force should have a focus on on Tanks and AT (i had two 4* Sherman Firefly and 2 3* M18 Tank Destroyers among others - forget US Tanks). Rather than starting a frontal assault, it prove to be key for me to escape southwards in the beginning - leaving the western key cities only weakly garrisoned (by the aux troops).
After several rounds the AI will start several attack waves after each other to the western cities with his elite armor - however each wave only consists of several armor pieces - and those you can kill effectively by flanking in from the south with your elite armoured core!
Even if you loose a key city, you should be able to recapture it, when flanking in. That strat was really key for me.
Meanwhile a small and highly mobile force (i used one self propelled Arty, two recon tanks, vanilla M18 + 2 British engi units) moves south quickly from the very beginning and captures on city after another in the south.
My airforce focused on the Panthers in the beginning and then assisted to defend my cities from some minor german pushes to my key cities in the bocage later on. (the ground units defending the bocage were Paratroopers and Recon). I have five fighters that chewed up the remains of the Luftwaffe with ease.

So i fought essentially with three battle groups.
1.)The mobile on going west to south quickly
2.) An armour focused one on the west to flank into the AI armour waves in the west from south
3.) And all the combined arms slowly hammering their way through on the east.
I hope that helps...