The sentence starts with two verb-ing modifiers — the second one containing a relative clause. The sentence structure is:

• Foraging at all times of the day and night, (First verb-ing modifier for the subject “a whale”. The whale forages at all times)
• but interspersing their feeding with periods of rest (Second verb-ing modifier for the subject “whale”. The whales — it has to be “whales”, not “whale” since the sentence uses plural pronoun “their” in the non-underlined part — intersperse their feeding with the periods of the rest.)
  • that last between one and eight hours, (relative clause modifying “periods of rest”. These periods last between one and eight hours)
• a sperm whale could eat so much as a ton of squid a day. (Main clause. Subject – a sperm whale; verb – could eat. The sperm whales can eat as much as a ton of squid a day)

The original sentence has the following errors:

1. We need to use plural subject “sperm whales” to match with the plural pronoun “their” in the non-underlined part.
2. The use of “could” doesn’t seem correct. When we use “could” in the present tense, it indicates possibility, not ability. For example: “this table can withstand 100 kgs” says that the table has the capacity to withstand a certain weight. On the other hand, “this table could withstand 100 kgs” means that that there is a possibility that the table will withstand 100 kgs. Here, within the context, it looks more reasonable to say that we are talking about the capacity or the ability of the whales. Thus, the use of ‘can’ is preferred. 
3. The idiom “so much as …” is only used in negative contexts i.e. when we have “not so much as…”. For positive comparisons “as much as…” is used. Please note that “as much as…” is also used in negative comparisons i.e. “not as much as…” is also correct.