No, there is no requirement to have revealed the whole map, nor even a significant portion. You might consider a start-of-game mid-battle level to take on, say, a level 3 foe by killing a level 1 foes and just preparing for the next hit. You should be able to do this by just finding few enough enemies around the start.
The only map revelation you need is enough to set it off and stand advantageous to defeat the opponent. This may simply mean exploring as much as needed to reveal your full chain of kills. After all, one of the other advantages of mid-battle leveling is that it does not provide your opponent any chance of regeneration.
Or, it might mean exploring some amount, then using a much higher attack power such that you still have dealt significantly more damage to the opponent than what it heals for exploration. Monsters heal 1 health per level per tile, just as you do. Setting up exploration-involved fights means having at least that much attack power above theirs. For example, if you want to use a 3-tile slot to gain just enough, you want to have at least a 30 point advantage over a boss so that you don't lose everything that you just did. To adopt this towards mid-battle leveling, you don't need to compare it to the enemy's attack power, and simply just need it so that the health you need to survive a mid-battle level won't heal the boss such that your damage is undone. The higher above their healing rate you can make your damage, the better.