Go to the EU PSN store, search for Destiny, pre-order it (for no immediate charge), and the Beta will begin downloading.
It will say that it has completed after downloading a small portion of it, but will continue to download in the background. To see the actual progress, navigate to the Destiny Beta tile, click the OPTIONS button, and select Information. You'll see a screen similar to the one in this post.
You will be able to play it on your main account in any region, so long as you go to Settings -> PSN -> Activate as Your Primary PS4.
Thanks to Dan27 for cancellation instructions:
Thanks to benny_a for bringing attention to what the SEN EULA says about pre-orders and cancellations:
OK. For PS4 clarification:
Pre-order the title. It will start downloading the beta.
Then go into: Settings -> PSN -> Account Information -> Wallet
Select: Transaction History.
You should see a Product Purchase in the amount of UK/Euro 0.00 from the date you preordered. Click on that Purchase entry
Select: Cancel Pre-order
That means you'll be able to download the Beta, and also ensure that the preorder is cancelled.
Please double-check that you don't have any money in your wallet and that you don't have a registered payment method that can be used to charge you.
You agree that for pre-orders of digital content products:
(i) we can charge you on the payment date displayed when you place your pre-order (if we accept it);
(ii) you or we may cancel your pre-order up to (but not including) the release date, in which case any sums deducted from your SEN wallet will be refunded (but this may not occur until after the release date);
(iii) we may make the pre-ordered products available to you on the release date and, once made available, as far as permitted by law, you will have no further right to cancel your order or to a "cooling off period";
(iv) when you cancel a pre-order you will no longer be entitled to any promotional services and/or products offered with the pre-order but if you subsequently access the service and/or product we will still charge you at full pre-order price; and
(v) you will not use your pre-ordered product until the release date, even if you are able to download it earlier.
When you place a pre-order, ‘Automatic Funding’ for your SEN wallet will be automatically turned "On" if you have registered a payment method (e.g. a credit or debit card). You can switch Automatic Funding "Off" at any time via your SEN account management page.