The assignment to write the `Rime of the Ancient Mariner`in the style of a dramatic monologue is designed to do two things, to show that you understand the nature of the dramatic monologue and that you have read the poem carefully.
A dramatic monologue is narrated in from a first person point of view in which the narrator is not the poet but rather a fictive or historical person. It can be addressed to a person (i.e. the wedding guest) or simply recount the narrator`s thoughts for the reader. Typically, the narrator should appear normal and trustworthy at the beginning of the monologue and only gradually reveal the dark or unreliable aspects of his nature.
In terms of the story, as this is a long poem, decide in advance what plot elements are essential, and what can be omitted. Also consider the order in which you wish to reveal information. Would a reverse chronological order, in which the narrator begins by portraying himself and an ordinary shipwrecked sailor, with the murder of the albatross revealed at the end be more in the spirit of the genre than a straightforward account?