The most common and most likely answer to this crossword clue is the 8 letter word SPLITTER
I've seen this crossword clue in The Daily Telegraph
S
P
L
I
T
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More clues leading to the result SPLITTER
Buddy explains!

The straight part
We know that "a terrible headache" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a terrible headache = splitter.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does SPLITTER mean?
SPLITTER noun- A person or a thing that splits.
- A quarry worker who splits slate into sheets.
- A scientist in one of various fields who prefers to split categories such as species or dialects up into smaller groups.
- A split-finger fastball.
- A draggable vertical or horizontal bar used to adjust the relative sizes of two adjacent windows.
- A wheaten cake split and buttered when hot.
- One who splits hairs in argument, etc.
- A device with two electrical plugs that plugs into an electrical outlet, effectively converting the electrical outlet into two; socket converter.