How are you suppose to beat the special units in the Gormanizer levels if you can only move 1 unit at a time?
Not sure what exactly your problem is, so I'll try to cover everything.
Basically: You have to move another unit with your active unit.
Just draw a small circle over four squares with another unit on it until it has moved in the desired direction, then move your "circle area" one square in the same direction and repeat.
Another tactic would be to drag your unit through a long line of other units repeatedly to have the entire "snake" move along.
Write off the first fleeing enemy if it's too far away, then eat a few attacks to set up your units properly in anticipation of the later waves.
Arrange your units in a grid pattern or something similar to achieve maximum combo potential and area coverage.
Use units with a high chance of special attacks.
Don't use units that have been slowed (clock debuff symbol). You can still move them with other units, but don't use them as your active unit.
Level up your team.
Also, units with sleep spells or ranged attacks may help?