This might sound like a lot of work, but I think it pays dividends in a lot of ways and saves time in the long run.

You might try writing a weekly email or memo on what you accomplish during the week and send it to your boss. It's clear that your boss doesn't realize how much you're doing.

Once you do it a couple times, the memos get easier to write. it's just a running list of things you accomplish (large or small) during the week. It doesn't have to go into minute detail and should probably fit on a page unless it's a crazy busy week, but it should highlight the important tasks accomplished, meetings attended, decisions made, decision outstanding and possible future projects. The memos will get repetitive over the weeks, but that's fine. Some tasks are maintenance. It still helps to add those tasks so the boss knows they're covered.

Before you go into these meet ups with your boss, you can email or give a copy to the boss to glance over so you're not covering ground that you already covered. That makes the time more efficient for both of you.

These memos are also helpful if new management comes in or if you're looking to justify a promotion.