Set the combat difficulty to the easiest setting. In Overlord mode, resources are rare and monsters are difficult. Your priority should be rescuing survivors. You will need to sacrifice them to slow down the onslaught. Perk token tiles and level up towers should be given a low priority until after turn 10. Some luck as to how the world map is generated will determine your success. Getting lots of survivors (especially soldiers) to fight is important. Building a few health clinics also helps, but they will not last too long. Save the game after each turn for safety.

Set the strategic level to the easiest setting. With each turn, the combat difficulty of each tile increases. Maximize your power to keep ahead of it. Beginning from turn 0, focus on any tile that gives perk tokens, followed by level up towers. Neither of those advances a turn. Try them as much as reqired. Besides the Overlord's Keep, the level up towers are the toughest tiles to beat. Always purify tiles to unlock the upgrade towers quickly before things get too difficult. Some of classes are useful for fighting horizontally, others are good for fighting upwards (towers), and some are good for fighting downwards (caves). If you cannot finish a tile with a certain mage class, try another. Change perks as required to match the new class. You do not need too many survivors; go after level up towers first. You can keep trying a tile repeatedly if desired. Because the map is randomly generated, you may not be able to unlock enough level up towers before the combat gets overwhelming. If this is the case, start over with a new map.