Look at the stats of the enemy to judge if your heroes are weak or strong against them.
The attack (sword), defense
(shield), and health (heart) stats are what you should be checking.
Your heroes' levels determines your health. Health is important as an indicator for your heroes' survival, but not the defining factor in winning a battle.
Every hero comes with base attack/defense stats, and from then on, their weapons determine their attack and defense stats. Powering up weapons increases attack and defense stats.
An easy way to compare stats is through the "Power" stat in the popup. Although it only shows the enemies in the first wave, it still might give an idea on how the battle will go.