The battle mechanic isn't too complicated but still can be confusing at first.
Battle Mechanics
Enemy's Attack - Enemy's attacks are triggered by a timer. Whenever the timer is up, the enemy will deal damage to the hunters. The 'speed' of timer varies between enemies from very slow to very fast.
Enemy's Signature Ability (SA)
Each enemy race has a SA like how Direwolf has Moon Howl. SA is triggered by the same timer of the normal attack. When the attack timer is up, there is a fair chance the enemy will trigger its SA instead of a normal attack.
Hunters' Attack - Hunter's attack is based on Hunter's base stat, weapon's stat and varied by the number of blocks matched. Hunters will trigger physical attack when Sword (red) blocks are matched or magical attack when Star (yellow) blocks are matched.
Hunter's Defense/Trap - Hunter's defense/trap is also based on Hunter's base stat, weapon's stat and varied by the number of blocks matched and charged. Shield (blue) and Trap (purple) blocks are matched and then charge to its tubes. Hunter will only trigger Defense then when the Enemy attacks/ and trigger Trap only when Defense failed.
Weapon's Signature Ability
Hunters gain SA from the weapons with maximum 4 weapons/SA equipped at a time. Similar to the enemy's SA, there are a fair chance (based on the number of blocks matched/charged) that hunters will trigger its SA instead of the normal attack, defense or trap.