The Raid
The Vault defenses will hit the entire row with the highest current health unit in it and raise its Defensive Barrier.
On higher difficulties, this attack will also apply a defense-lowering debuff, Hull Shred, to all units hit, which becomes more severe at higher difficulties.
After this attack, The Vault will be protected by the Defensive Barrier until the end of the round, which increases the Security of the Vault as well as offering it Damage reduction.
The Security and damage reduction caused by the Defensive Barrier increase at higher difficulties.
On Brutal and Nightmare difficulties the Defensive Barrier will also be charged as indicated by the big energy orb.
Attacking before it is too late will remove this charge, otherwise, it will explode causing damage and applying Hull Shred to all units.
Every third round the Vault defenses Charged Attack will hit your entire team, apply the Outgoing Damage Over Time Down 2 debuff to them, and cause Lose Charge (1).
Every round the vault will gain a stacking damage increase buff, Reactor Overcharge. Starting from round 20 the Vault will gain a stronger version of this buff. The power of these stacking buffs increases at higher difficulties.
Summary
All debuffs and damage have to be done fast at the start of each round, while protecting your defenders and keeping your team alive. At higher difficulties, the Overcharged Barrier also has to be attacked after it appears.