This is basically what I can recall:
The Battle Phase is split into 3 steps:
1. ATTACK/BLOCK DECLARATION
2. DAMAGE CALCULATION
3. POST-DAMAGE CALCULATION
1. DECLARATION is split into the following steps:
    1. Turn Player chooses Attackers
    2. Turn Player can use any cards with  'When you attack' Triggers
    3. Opponent can use any cards with 'When attacked' Triggers
    4 Opponent declares Blockers
    5. Opponent can use any cards with 'When blocking' Triggers
    6. Turn Player can use any cards with 'When blocked' Triggers
    6. Attackers are rested (Adamant/Vigilance Check?)*
    5. Blockers are rested(q: does blocking rest?)
    6. Move to Damage Calculation (unlike YGO no triggers for replay)
2. DAMAGE CALCULATION
    1. Total Attacker's DMG Value
    2 Total Defender's DMG
    3. If Total DMG >= 0:
        If list of defending blockers >= 0:
            Player Chooses a Blocker:
                Total DMG = Total DMG - Target Blocker ARM
                Check for 'ON_DEALING_DMG' & 'ON_DEALT_DAMAGE'
                Check if Blocker can be destroyed by battle:
                Del Blocker from Field
                Add Blocker to Discard
                Check for 'ON_DESTROYED' and 'ON_DEFEAT' for BLOCKER
        if list of defending blockers <= 0:
                If Pierce:
                Defender Life = Defender Life - Total DMG
                Check for on 'PLAYER_TAKE_DMG' & 'DEALT_PLAYER_DMG'
    if Total DMG <= 0:
        if list of defending blockers > 0:
            Repeat Step 3 in Reverse
3. POST DAMAGE CALCULATION
    TRIGGER_CHECKS FOR: ON_SENT_TO_DISCARD, ON_DESTROYED, ON_DEFEATED, ON_DEALT_DAMAGE, ON_BATTLE etc.