Is there an implied verb missing?

Is this statement correct? -

However catastrophic the physical abuse, the lasting scars came from the verbal insults that had been hurled at them.

Does the first part of the sentence before the comma need the verb "was"?

In answer to the question in the OP's headline, yes there is an implied verb in the phrase "However catastrophic the physical abuse"—and since it is implied, it is of course missing. But conceding that the phrase omits an implied verb isn't the same as saying that the author erred in omitting it.

Given that the next part of the sentence uses the verbs "came" and "had been hurled," I think we can safely discard many of the possible verbs suggested by Hans Adler in his answer. I also think that the gist of the opening phrase is all we need to understand in order to make sense of the sentence as a whole: Trying to ascertain whether the precise verb or verb phrase that the author had in mind was "might have been" or "may have been," for example, simply isn't worth the effort.

The larger point is simply that, in the author's view, the metaphorical scars from the verbal abuse that "they" suffered lasted longer and thus were in some sense more difficult to get beyond than the actual scars from the physical abuse that they endured—even if the degree of physical abuse involved was highly catastrophic.

A verb is definitely not needed here, though it could be added without changing the meaning. The part before the comma is a (conditional) subordinate clause, coordinated with the main clause by the conjunction however. It is here used in the sense regardless [of] how, no matter how, irrespective of how, ....

Only the verb be can be dropped in this way from certain subordinate clauses, but then it can be dropped in all tenses and aspects. If we want to add it, we have many options that all differ in meaning:

• However catastrophic the physical abuse is, the lasting scars came from the verbal insults that had been hurled at them.
• However catastrophic the physical abuse was, the lasting scars came from the verbal insults that had been hurled at them.
• However catastrophic the physical abuse has been, the lasting scars came from the verbal insults that had been hurled at them.
• However catastrophic the physical abuse used to be, the lasting scars came from the verbal insults that had been hurled at them.
• However catastrophic the physical abuse had been, the lasting scars came from the verbal insults that had been hurled at them.
• However catastrophic the physical abuse will be, the lasting scars came from the verbal insults that had been hurled at them.
• However catastrophic the physical abuse would be, the lasting scars came from the verbal insults that had been hurled at them.
• However catastrophic the physical abuse is going to be, the lasting scars came from the verbal insults that had been hurled at them.
• However catastrophic the physical abuse was going to be, the lasting scars came from the verbal insults that had been hurled at them.
• However catastrophic the physical abuse may be, the lasting scars came from the verbal insults that had been hurled at them.
• However catastrophic the physical abuse may have been, the lasting scars came from the verbal insults that had been hurled at them.
• However catastrophic the physical abuse may have been going to be, the lasting scars came from the verbal insults that had been hurled at them.

If we want to restore the omitted verb, we need more information than the sentence currently provides to pick the right one. Omitting be in this way is shorter, moves attention other, perhaps more important parts of the sentence, and can be used to express uncertainty or even to be ambiguous.