Funny enough @TotalTSI've been working on this on and off over the day and I've come to the conclusion that it is nearly impossible to get the correct DVs for this Mew with just the picture. There are way too many assumptions that need to be made especially if the picture was only for publication. My first assumption was that it was like every other classic Mew distributed at the time with a DV spread of:
HP = 5
Attack = 10
Defense = 1
Speed = 5
Special = 12
However, at level 39 the stats would not match that of an untrained Mew at the level which would mean that the Mew would have to have been in battle meaning that it would have acquired EVs. That said the possible EV spread for a Mew with the normal DVs and to have the listed above stats would be:
HP = 961 - > 1848
Attack = 0 -> 8
Defense = 16129 -> 18224
Speed = 0 -> 8
Special = 1849 -> 3024
But, the issue here is the attack and special DVs are 0 -> 8 which is impossible consider the other EVs. The second assumption would be that the person leveled it up using Rare Candies and Vitamins and again that would be impossible since vitamins increase the stats EVs by 2560 points in gen 1 and the lowest possible HP EV is 1848. That would mean that the Mew was in battle and since the attack and speed EVs would be impossible for a Pokemon that saw battle which would mean that this Mew has a different set of DVs then the ordinary Mew given out at the time.
So now that it is clear that this Mew has a different set of DVs then the known Mews what are the DVs? Well this is where the largest unknown of the equation comes into picture, how was this Mew trained? Just to get the first major hurdle out of the way the Mew in the picture has been trained. There is no DV combination that will give an untrained Mew at level 39 those stats considering the picture shows a defense stat of 96 when a Mew at the same level with a DV of 15 and EV of 0 will only have a defense stat of 94. Thus, the Mew has been trained. Now the question is how was the Mew trained? For simplicity I've come up with 4 possible scenarios for how the Mew could have been trained.
Scenario 1 - Rare Candy and Vitamins: The problem here is we wouldn't be able to determine how many time the Mew was given vitamins.
Scenario 2 - A new game file and the Mew was obtained as early as possible: This would be easy to test with putting Mew into every battle until it is at level 39. However, the problem with this scenario is that Nintendo Power needed a trained Mew for the picture and this method would probably take too long to get the desired result and the badge level cap for Pokemon obeying the player would probably be an issue. Therefore, probably unlikely.
Scenario 3 - Got the Mew mid-game and trained it to level 39: Again easy to test, but the issue is badge level and slow in actuality; therefore, unlikely.
Scenario 4 - Got the Mew at the end of the game and trained it to level 39: This one is the most believable scenario in my opinion since it would be fast due to high level wild Pokemon. However, there is still some unknown factors that would prevent someone from training a Mew to level 39 and then adjusting the DVs to match the stats in the picture.
Even with scenario 4 sounding the most promising to find the DVs the next biggest issue would be what level did the Mew start at. Did they get it at level 5? What about level 10 or even level 15? We just don't know which makes the task at determining the DVs at this present moment all that more impossible. As well, non of my outlined scenarios might be right or could be a combination between then. We just don't know what the DVs of the Mew in the picture without more personal information about the player of that save file. Thus, bring me back to my opening statement that it is nearly impossible to find the DVs of the Mew just from the picture alone. Others are still welcome to try and determine the DVs, but this is just my take on the question and I could be missing an obvious piece of information that would make this task trivial.