Bit more work on Tutorial from would have helped I think :). Wall of text only helps so much. But you know how it is with Jams :D ran out of time.
the key bit is in the battling other tiles, the more sides you have flanking the tile, the better your attack will be, and thats the 4 main sides, not diagonals. If you're hitting only 1 side, your loose troops 2(yours)-1(theirs), if on 2 sides, its 1-1, and 3 sides 1-2 and 4 sides 1-3. Sometimes you have to force your way in, so you'll need to up your multiplyer and brute force into a tile even if its only 1 side, to then work along the row.
Thanks of playing! how that helps