Hey All,
While Angel's explanation is entirely correct, it's a bit light on detail, so I thought I'd weigh in.
The big category here is modifiers, and the rules regarding modifiers are very strict. If you want to modify a noun, the modifier and the modifi-ee (my invented word) have to touch.
(A) encounter native crocodiles lurking in the shallows, whose eyes and noses are peeking out
(B) encountered native crocodiles lurking in the shallows, whose eyes and noses peek out
(C) had encountered native crocodiles lurking in the shallows, whose eyes and noses peek out
(D) encounter native crocodiles lurking in the shallows, with eyes and noses peeking out
(E) encounter native crocodiles lurking in the shallows, with eyes and noses that are peeking out
The first split you inevitably saw (aside from the verb tense issue up front, which we can also discuss) was "whose" versus "with". "Whose" is a relative pronoun, and can only be used to modify nouns. That means that "whose" better go RIGHT NEXT to the thing it modifies. Unfortunately, in A, B and C, it modifies "shallows". This doesn't make any sense, for obvious reasons.
"with" is a preposition, and also sets off a modifying phrase. However, this phrase is not modifying crocodiles (As you may have assumed) but "lurking". One way to determine what's being modified is to ask yourself what question is being answered by the modifying phrase. In other words, you can't answer a question about the crocodile with this modifier ("What were the crocodiles doing?" "With eyes and noses peeking out" -- this makes no sense). But you can answer the question "How were the crocodiles lurking?" "With eyes and noses peeking out"). We're modifying a verb, and verb modifiers DO NOT need to touch the verbs they modify.
Between D and E, D is simply more concise (there's no reason to introduce the relative pronoun "that"; it just complicates the meaning).
Also, there's no reason to use any tense but present here. Notice the original verb "participate", which is in the present, then ask yourself if there's any good reason to change tenses. There isn't. Answer is D.
Hope that helps!