Not entirely sure where the 'shaming' kicks in, but the purpose of that forum is specifically to resolve issues with the rules, not as a means to gain access to rules you don't have access to right now. For that kind of help, you'll likely want to ask in the Roleplaying forum, where I've moved this thread.
So, on that note, regular Elementals have 10 points of TW scale armor.
The table on p.187 indicates this works as 9/8/8/8. But it being Battle Armor, it works a little different than regular body armor rated at those values.
A Sunbeam does 4E/4. Let's say you also got a MOS of 4 for another point of damage.
You're facing BAR 8 armor for energy, so the difference between the gun's AP of 4E and the armor is 4. So your Damage is reduced from 5 to 1. If it wasn't for the MOS, you'd do no damage at all.
That 1 damage is then divided by 8, the BAR of the armor you're striking, just as if you were shooting a vehicle. You do 0.125 damage, which rounds to 0. Drat, no damage at all.
Note that tactical armor doesn't degrade like regular armor. That Elemental's BAR will stay 9/8/8/8 until you whittle away its last point.
Also, attacks that do subduing damage do nothing to Battle Armor.
Finally, if you do manage to cause damage, the operator of the suit also suffers damage. He suffers the damage you did to the suit -1.
Let's say you're firing an SRM at it. That's Class E ordnance. Let's say you're using anti-vehicle rounds, so 8X/12A.
It's BAR of 8 matches your AP, so you do 12 damage + anything you might get from MOS. Let's say your MOS was +4, enough for +1 damage. 13 damage total.
That's then divided by the BAR of 8 for 1.625 damage, which rounds to 2 damage. The operator suffers that 2 -1 damage, so takes 1 point of damage.
Another alternative is to use the Battle Armor critical rules found in ATOW:C, which can allow you to degrade a battle armor's functionality even if you haven't blasted all its armor away yet.