Here is the full list of all 20 Field of Glory II achievements.
Failed a cohesion test when only snake eyes would have failed
You won your first battle!
Killed an enemy C-in-C
Made an enemy unit autodrop cohesion from a flank charge
Won a battle on Emperor difficulty
Won a battle on Deity difficulty
Won a battle with Romans on at least Legate difficulty
Won a battle against Romans on at least Legate difficulty
Won a battle with a cavalry army on at least Legate difficulty
Won a battle with a pike army on at least Legate difficulty
Won a battle with a Slave Revolt army against Romans
Won a campaign
Won a 15 battle campaign
Created a Multiplayer challenge
Fought a losing Multiplayer battle to completion without conceding
Won a Multiplayer battle
Rallied a routing unit with a general
Routed enemy elephants by shooting
Made a unit drop cohesion from artillery fire
Passed a cohesion test when only double six would have passed