No pictures, and unfortunately the scale was such that we couldn't game out the entirety of the battle.
However, broad strokes:
The defenders turned out to be much tougher than expected.* The projections were technically (mostly) accurate, but the details, which the Ice Hellions only fully learned when the battle was joined, were much harsher than expected.
The initial clash saw a battle between a company of manticores and two stars of omnimechs. Meanwhile, the Ice Hellions identified the commanders and dropped a star of elementals on them. This command post turned out to be the same four mechs that had defeated the previous invasion (two phoenix hawk LAMs, a Griffin, and a heavily modified commando), except that they'd managed to upgrade their machines with a few clan tech weapons. One of the LAMs had also traded its machine guns for a pair of bomb bays and managed to kill two points outright with fuel air bombs. After losing half of their forces, the elementals requested hegira, but were denied and then wiped out. The elementals damaged three of the four mechs, one fairly badly.
The loss of the elementals led to the first break in the bid, which saw additional elementals called down. The hellions then advanced into the city. The defenders relied heavily on a mixture of SRM Carriers, Hetzers, Saladins, and field gun equipped infantry, and while the clans had air superiority and could move about the city at will, each strong point was murder to clear out. Additional reinforcements (second line mechs, the rest of their elementals, and a few points of aerofighters to hunt artillery) allowed them to win out.
The second headhunting strike was launched against the militia command center in the middle of the city. Three points of elementals were dropped on the roof and started killing their way down, forcing the command staff to evacuate through underground tunnels to other bases. Once the command staff was clear, the defenders blew out the bottom of the building (using stored ammunition in the nearby mech bay) and dropped it on top of the elementals.
Another unexpected element was a contingent of pirate mechs that had apparently sought sanctuary on Somerset. Half of these deserted and attempted to surrender shortly after the Hellions land. Some more were killed, but one suspiciously well equipped lance fought very well, then withdrew to a hidden ship after the city fell. Recovered records revealed the commander of this lance was named Tasha Kay ( ;) ), but nothing else about them.
After the city fell, the Ice Hellions took the Somerset Academy without resistance. The training battalion was kept out of action by order of the commandant for some reason and withdrew into the wilderness. The defending commander and his or her (depending on who you ask) immediate staff left the planet soon after, but their ship was so small that it could only carry about a lance of mechs anyway.
All told, the total Ice Hellion force included two front line mech stars, three second line mech stars, five elemental stars, one vehicle star (which mostly didn't see any action) and three points of aerofighters.
The defenders basically lost their armored forces, artillery, and field guns in the capital battle, but still fields considerable light infantry assets that will have to be cleaned up, plus the training battalion. Their senior leadership has left the planet however, and the Commonwealth government has already sent a ship to evacuate the training battalion.
*The composition of the defenders was determined by Monbvol, who is playing the character of the planetary ruler, and had the defense budget appropriate to a character with a world as a landhold to work with (discussed in A Time of War Companion)