A Burke could take on three missiles no problem.
One thing to note is it was not being hit with anti ship missiles even a normal anti tank missile is unlikely to do siginficant damage to a naval ship. The armor is thick enough and the ship is big enough that even if the missile makes a breach its unlikely to have enough reach to hit anything vital. So it is likely it could take more than a few of a hell fire equivalent type missile. After the first missile was launched though only TV that allowed the rest of the helos to survive more than a few seconds as the phalanx guns would have tracked and engaged and ripped them to pieces in seconds once the free fire was triggered.
Modern warships have little to no armour besides kevlar to trap splinters.
A boat filled with explosives is way more dangerous to a destroyer than an anti tank missile would be. It hits at the water line on a low to non angled surface so the armor there is less than impacting off the front armor on the main superstructure. Had the helos been launching anti shipping missiles from that close of range it is unlikely it could have survived one let alone multiples. But old soviet hellfire equivalents would probably cause some damage but mostly superficial and repairable.
Anti-Tank missile won't do much but case a ton of splinter damage and shred up electronics and wiring. Depending on where it hits it could be little or a lot.
ASMs big danger depends on how much fuel it's still carrying by the time it strikes. Fire is a ships #1 danger, though that danger has been mitigated in recent years by the return of steel hulls, though aluminium is still used in superstructures to keep top weight down.
Anti-tank sized missiles are only used for small boats though these days dual use SAMs are used more then ASMs for a variety of reasons.
In an engagement between missile cruisers like that, the victor would be whoever could lock and fire first; the CIWS are effective but not against a full spread.
Aegis and VLS tubes allow a Burke to target and engage as many targets as it wishes. The only limit to the system back in the day was it being tied to the old launchers that had to reload, now that's not an issue.
CIWS is shit for engaging missiles and always has been, It's only good for taking out boats and even then a Phalanx chews through ammo too quickly.
The issue with CIWS is that by the time bullets can hit a missile that missiles already so close that the debris will continue on and impact the ship.
Those Kirov class boats are old as fuck.
They were designed to guard Soviet sub bastions and carry as many ASMs as they could to fling at Carrier Battle Groups before they died, most like before they got anywhere close enough to launch their missiles.
They weren't great in the Cold War and they're worse now after the treatment they've received rotting all these decades. They're still good to counter most foes Russia might meet, most likely using tired old ASMs they gave them and training their crews, especially their nukes so their experience isn't lost.
Well, to be fair, the movie does state that was combined with a form of fusion.
That's BS and you know it. It's like saying I make fires out of inflammable shit in combination with heaping gallons of gasoline.
