So, back at Denmark Strait: Eugen was never in any doubt Hood was firing on her - moreover, Hood was by far the closer of the two attackers, within far easier range of reply for Eugen's 8" guns. German after-action reports of the gun-duel describe Eugen's shooting as "exquisite" - not "good", not "effective", but exquisite - which can only mean multiple hits, achieved early and often. Indeed, it seems generally-agreed that among the very earliest of Eugen's salvoes, a shell(s) from at least one (the 2nd or 3rd) struck Hood's boat deck, starting a fire - described as "large" by the Germans, thinking it involved (floatplane) avgas - which raged unchecked, producing considerable smoke. Another fire was apparently started by (at least one) hit(s) forward, at the base of Hood's bridge/conn, and as well her foretop was shot away. That sounds like a good descripton of "exquisite" shooting, (all) by Prinz Eugen.
Of course, any account ultimately crediting the sinking of Hood to Bismarck must have some way to introduce the latter into the gunfight between Eugen and Hood - but I have yet to see any credible evidence for it, and - far more compelling - it would have MADE ZERO SENSE. Because with the onslaught also of a KGV-class BB - as which POW was correctly identified on the spot, by the Germans, although thinking she was "King George" herself, and so of course knowing nothing of inoperable Vickers turrets, etc. - her threat of a forward-firing salvo of six 15"-ers (and 10, if she could maneuver to bring all guns to bear) was, by far the greater - especially TO BISMARCK - compared to the threat from Hood (also correctly identified on the scene), already being engaged by Prinz Eugen and even set on fire. Moreover, the greater range of Bismarck's 15"-ers' - and position trailing Eugen, putting them just that much (slightly) closer to the "King George" already - gave her every reason to target POW over Hood. Which is, I believe, exactly what Bismarck did - also better explaining the many hits ultimately suffered by POW - in the ballpark of 10 all told, if I understand correctly - over the course of the entire battle.
If the above is correct, then already by process of elimination Eugen must have sunk Hood. Indeed, the only detailed "evidence" crediting Bismarck for this feat are all anecdotes - recounted well after returning to port, of course - which are nevertheless so explicit (the ONLY items coming out of this entire story to be so explicit, and self-assured) as to be almost defensive in nature, and already suspect just on the face of it. Add to that they all came from RN officers, and any last shred of credibility must be challenged - as I agree with Don that Hood's loss was immediately and profoundly a national (actually, an imperial) embarrassment of major proportion, giving the British a powerful motivation to "spin", as much as they could, Hood's catastrophic and utter destruction as a "lucky strike" by the most formidable of all German combatants: Bismarck. Such is to be expected - again, the SIMPLEST interpretation - of a POLITICAL HISTORY: one primarily written by the British - as (one of) the Allied ultimate victors of the conflict overall - but even more urgently in the days immediately following the sinking, with the final outcome of the war itself still very much in doubt. Then, a few days later - with the loss of Bismarck - the Germans would be given an almost identical national/political motivation to push exactly the same, "face-saving" story: that Bismarck was lost, but not before taking down the Mighty Hood.
How embarrassing - for both sides, but particularly the British - to instead have recognized that a feisty little Prinz Eugen (in actuality) "got lucky", and managed to take down the Hood. Especially again regarding the RN, considering they also had two of their own 8"-gunned cruisers standing by, yet contibuting essentially squat to the battle. And finally also for the Germans: to have lost Bismarck for essentially no achievement whatsoever. (Except as bait, to lure Hood out under Prinz Eugen's indefatigable guns!)
As to precisely HOW Eugen pulled it off, the whole debate about her 8" shells vs Hood's armor vs plunging trajectory is, I believe, not essential: everyone agrees that, from very early on, she SET HOOD AFIRE. A fire can certainly kill a ship - and a fire that reaches a magazine can do so catastrophically, exactly as observed for Hood - without requiring any further hit(s) whatsoever. Hood's boat deck fire, in particular, engulfed ready-use ammo lockers for both 4" High-Angle gun and UP rounds - either of which, popping off and rocketting down the wrong scuttle and into a powder bag, would have signalled Game Over. This is the SIMPLEST explanation - and, all other things "being equal" (i.e., vague and unknowable, as they are) also the BEST explanation, IMHO - of why the shootout between Hood and Prinz Eugen suddenly ended in the devastating explosion of Hood.
However, as for HOOD's shooting - and the attribution of all the (three) hits on Bismarck to Hood (and not POW), I will disagree with Donny here - again, largely per my Axiom-I above, now considered from Hood's point of view: not only BEING SHELLED but already even HIT by Prinz Eugen, she had zero reason to redirect and lob irrelevant shots at Bismarck, but instead to intensify targetting to wipe out her smaller, yet dead-eyed-shooting tormenter ASAP. For which her turn to bring all 8 main guns to bear can very believably be ascribed - but which end goal she never managed to achieve, before exploding. Therefore if true then again by process of elimination, any hits on Bismarck must have come from POW. And in the scenario of Bismarck engaging POW from the very beginning, above, this is now again consistent with Axiom-I for POW: she would certainly focus her fire on the one - Bismarck - who was SHOOTING AT HER. So, I see the least amount of evidence for HOOD having hit anyone - certainly least of all Prinz Eugen, whom she desperately needed to knock off her back. Instead, (one thing and/or another in) the cumulative damage wreaked by Prinz Eugen's 8" guns ultimately blew up the huge battlecruiser.
Followed within days by the Germans' loss of Bismarck - their most powerful battleship - doomed to destruction essentially by a skinny 17" torpedo, lugged beneath a lumbering, fabric-covered biplane, to be dumped at low speed off her stern. Exquisitely.
Unbelievable - you couldn't make this sh** up!
And finally Prinz Eugen - in typical "Life of Riley"/"Winner-Take-All" fashion - lost no lives, nor even casualties or damage of any kind - made a clean and complete getaway from the entire stirred-up RN hornet's nest in the Atlantic - and even survived the remainder of the war, in perfect condition. In the end, the Allies' anchoring her at Ground Zero for the Bikini A-bomb test was no doubt also more than a little bit Political, in nature - perhaps even a subtle admission they knew she WAS the one who sank The Hood, Pride of the British Fleet.
I had long wondered why Airfix, among so many crude, even "doggy" early ship kits - including their 1/600 Bismarck, and even their Hood, to some extent - at (about) the same time, produced a truly gorgeous and detailed mold of Prinz Eugen: someone over there clearly put in substantial extra work to do justice to the depiction of "little" Prinz Eugen. Now, in a first-time ever for me, Don has perhaps offered us the reason why...
(P.S.: Airfix' 1/600 KGV kit is also unusually crisp, detailed and - just like their Prinz Eugen - apparently highly accurate, as well.)