The regeneration rate can be increased via research

Monster Hunt is a feature which allows players to attack monsters which spawn on the Kingdom Map. Players must be in a Guild to hunt monsters. Each player can only send out one hunting party at a time. A monster hunt is like a standard hero battle, and the results are computed instantly. Players can watch the replay of the hunt by clicking the appropriate button in their message system Players can send 1-5 heroes on a monster hunt. See the individual monsters for specific hero lineups. The recommended hero lineups will often vary, depending on the monster level. The most commonly used hero types are Physical and Magic. Strength heroes are rarely used, as they are mostly used to hunt Level 5 monsters. Monster Manual Tap on the information icon on a monster, to view the Monster Manual. This will display the monster type, and the type of heroes players should use against it. It's better from a pure damage perspective to send multiple attacks without damage boost, until the maximum DMG Increase bonus is reached. Doing so will however also increase the risk of someone stealing else stealing the kill.