You cannot achieve Perfection without getting into Qi's room and his endless grind. So to your question 'when will you achieve' the answer is 'never, for this reason'. However, if you want an even more on-topic rant, then I've got just the one for you, my friend!
Everything the Perfection quest asks for is pure grind. Ship one of everything, make one of everything, catch every fish, cook every recipe (which means obtaining every recipe which means it isn't even obtainable before the end of Y2), max hearts with everyone, find all the walnuts... it's a boring pointless grind for the sake of boring pointless grind. And in many cases, directly counterproductive to actually playing the game.
The problem is that you have all these optional things you can do if you feel like it, included with the knowledge that not everyone is into it, and very very few people will ever do them all. Now suddenly they aren't optional anymore if you want access to actual content. Which is lazy coding at its worst. Let's take a look at the numbers, shall we? This is from the Steam Achievements page, which granted isn't the entire userbase, but is a large enough percentage to be representative for our back-of-napkin calculations.
Many of these 'perfection' milestones are already achievements, which makes the numbers easy to look at:
* Master of Five Ways (getting skill 10 in all skills): 9.7%
* Legend (earn 10 million gold) isn't exactly getting the golden clock, but that is the price tag on said clock, so we can give the benefit of the doubt and use it as a stand-in: 5.4%
* Full Shipment: 2.9%
* Master Angler: 2.9%
* Protector of the Valley: 2.5%
* Gourmet Chef: 1.5%
* Mystery of the Stardrops: 1.3%
* Craft Master: 1.1%
So you took all these achievements, and made them mandatory to unlock additional content. You took the second rarest achievement (second only to Fector's Challenge) and locked content behind it!
So congratulations, to that likely less than 1% of all players (since one must have ALL of them, not just any given one) who are able to achieve Perfection. And these are the stats at least a month after the 1.5 launch, which likely encouraged at least some people to go through and complete them just to see what happens when you do.
This is poor game design at its worst, locking content behind pointless achievements that 99% of the player base will never see.
There, is that on-topic enough for you?