Work the two components in parallel:

i) The content
@ 2-3min / slide you need 5 slides for 15min: 
- well crafted, each delivering a single key message
- flowing into each other naturally
- forming together a compelling story

ii) The delivery
- Rehearse out loud going over your slides (many times)
- Time and record your self (for added pressure)

--
Personal experience

What is appreciated: 
- Poise
- Rhythm 
- Engagement with your audience 
- Making it seem like a conversation and not a download / dump of information, i.e. opening doors for subsequent discussions - the best presentations are the one I interrupt halfway with a question and the exercise becomes a discussion.

What looses a senior audience:
- Talking about process rather than results
- Highlighting unimportant details
- Going off on a tangent

First of all, before being structured and top-down you have to know what key messages to convey. 
Your key messages have to pertain to the content the interviewer gave you and have to be insightful and helpful to solve the problem. 

You usually start with a question, like “would you invest or not in this business? If yes, at which conditions?”. 

Keeping that question in mind, you read through the material provided to you and try to extract the key messages that help you answer the above question. If you find something that is not totally relevant to the question you are solving, but you still consider it relevant, keep it in mind.

Once you've finished reading the material, review the key messages you have extracted from the text and link them in a story. This means that your key messages have to be either

• a summary/introduction on the issue or context of the case
• connectors from two different pieces of intelligence (e.g., sales in China grew by 20%, while in the rest of the world by 6%; why? Maybe because in another slide they say that China introduced a new business model to sell the product)
• something that is bringing a problem to the overall story you are gradually collating; in that case, if you understand why it is so you usually make a significant leap in understanding

Now that you have something intelligent to say, you can focus on conveying it in a structured top-down way. 

On this, Charlotte's comment makes a lot of sense because she highlights a process to assemble a short top-down presentation. 
That said, my humble suggestion is to focus more and more on what you say. If your argument is connected in a story, has business meaning, generates insights, and gives you the opportunity to answer your overarching question, finding structure is almost immediate. 

(edited)

Hi there, 

this is like writing slides, it is not in reality about the slide, what you think is the most important to say. 

you have 15 min which is not much, hence you have to go the 80/20 approach. I always recommend starting with an executive summary, allowing the readers to understand what they can expect. 

Then you unfold the whole story. To make the story, I would recommend using the BCG SCQ framework:
 

• Situation: what has been known (e.g. Company X has been the leader in the market for the past years) → people often miss this part as they think it is so obvious, everyone knows it, but in reality, without this info, you have no story
• Complication: What changed the status quo (e.g. in the last year a new competitor entered the market and dropped price significantly, which resulted in the loss of our client largest account)
• Question: what are you solving for (e.g. we are addressing how our client can respond with its pricing strategy)
  Once you identify your SCQ you will be able to get your story out. Remember C level don't go to detail, high level, the main impact messages

you can practice with you family or friend who is out of the business telling them stories about cases you solve. If they understand you, you are fine, if they dont, you have shape your skills. 

If you would like to learn more, please feel free to reach out, this is a topic I also teach new hires at BCG. 

Good luck,

Lucie

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Hi there,

This is a far more complex/nuanced topic than can be covered in a Q&A! I highly recommend you reach out for professional coaching in this area.

The main things to keep in mind are you need to be structured, concise, precise, and make sure to always be speaking on topic (i.e. about the items that answer the question).