The real source of the ambiguity here is the lack of what’s known as a complementizer [1]—such as the relative pronoun that—to delineate the relative clause boundary, as @xtacy implies with his last option. English happens to allow this slot in the syntactic tree to have no overt realization [2] [3], but when it goes unfilled with anything but trivial relative clauses it can introduce ambiguity.

As an aside, this particular sort of syntactic ambiguity happens to largely arise in the context of newspaper headlines—just as has happened here—since complementizers are generally dropped in telegraphese. These ambiguous sentences are so common that they have their own term: ‘crash blossoms’ [4].

Here are the two potential parse trees with an empty complementizer:

1) [Diver snaps [first photo [of [fish using [tools]]]]]
2) [Diver snaps [first photo [of [fish]]] using [tools]]

The incorrect parse is (2). In any event, disambiguating it is simple—just add an overt complementizer: ‘Diver snaps first photo of fish that’s using tools’. You can see why this disambiguates:

3) [Diver snaps [first photo [of [fish [that is [using [tools]]]]]]]
4) * [Diver snaps [first photo [of [fish]]] that is using [tools]]

Here (4) is ungrammatical because in English snap isn’t a verb that accepts a clausal complement (unlike a verb such as, say, think or persuade), thus you don’t parse the sentence that way and (3) is the only possible interpretation. Cf. (5, 6): there’s nothing I can come up with to put in the relative clause that would make the sentence even remotely grammatical. My interpretation of (7) is that it’s marginally acceptable (perhaps in a specific context: ‘What do you snap with your camera?’ ‘Oh, I snap that flowers bloom.’) but snap in (7) is intransitive whereas the snap we’re discussing is transitive.

5) I think that Hiroki Narimiya is awesome.
6) * I snap photos that flowers bloom.
7) ? I snap that flowers bloom.

@ggchappell: The parse where the photo is the one using the tools (shown as (8) below) may from a purely tree-parsing standpoint be theoretically possible, but from an actual linguistic point of view I doubt you could typically elicit such an interpretation from an actual speaker. An actual syntactic distinction is often made in language between animacy and inanimacy [5]. In traditional syntactic theory, the verb use has an argument structure [6] requiring an agent; but since a photo is inanimate it’s not marked as an agent and thus cannot provide the verb with a subject, violating various hypothesized syntactic rules and making the parse unacceptable.

Compare (9) below, which is acceptable. The relative clause is passivized, and thus the subject of the clause (the photo) is the theme rather than the agent and there’s no problem.

8) * [Diver snaps [first photo [of [fish]] [that is [using [tools]]]]]
9) [Diver snaps [first photo [of [fish]] [that can be developed]]]

See, I always knew that graduate degree in linguistics would come in handy for something!

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[1] http://en.wikipedia.org/wiki/Complementizer

[2] http://en.wikipedia.org/wiki/Relative_clause

[3] http://en.wikipedia.org/wiki/Reduced_relative_clause

[4] http://en.wikipedia.org/wiki/Syntactic_ambiguity

[5] http://en.wikipedia.org/wiki/Animacy

[6] http://en.wikipedia.org/wiki/Theta_role