I would say it's the other way around. It's very likely they will always be obtainable. If these were limited-time only, it would be made much more clear, like with other content that is intended to be limited-time from the beginning. There are far too many of these achievements for SE to expect people to get them all before the next phase reasonably, and there is no reason to believe you won't be able to still get them during the next phase. Now, the actual turn-ins will likely give barely any skybuilder points or scrips, much like how they reduced the rewards on the original turn-ins, but you will most likely still be able to acquire and turn-in the mats/crafts for the achievement, much like how you can still craft and turn-in first-phase items. Not sure how they will handle the gathering mats, but I assume they will either add new nodes, or add more items to existing nodes or something along those lines. If they replace the old mats I assume they will somehow keep the artisanal mats intact, since those are what are required to craft the achievement crafts. It is also perfectly reasonable to expect the achievement and its description might simply be updated come 5.3 to also include phase three items.
Basically I find it highly unlikely they would add a giant pile of time-consuming content, achievements and rewards then immediately remove the content and make them unobtainable the very next patch. That just sounds completely ridiculous to me. They removed the first-phase gathered items, but then again, there was literally nothing tied to the first phase content at all. No achievements, no log completion, no nothing, so nothing was lost by their removal except the occasionally amusing item descriptions (seriously, ishgard restoration items often have hilarious item descriptions, if you don't normally read flavor text, you should check them out lol).
Either way, this is definitely one of those things they should make perfectly clear ahead of time since the uncertainty of it just stresses the hell out of people and makes them play the game in unpleasant and unhealthy ways out of fear for no good reason. They did this with the previous diadem and I honestly will never forgive them for the way they handled that. It was completely unacceptable and they should be ashamed of themselves.
One more addendum: If you are really worried about these achievements going away, what I would do is work on the gathering ones and do them, and make sure you gather enough mats along the way to do the crafting achievements later (you will absolutely have enough mats to do all 8 crafting classes by the time you get the gathering achievements). While there is a chance they will remove the gathered mats like last time, I guarantee the crafted recipes and turn-ins will still be there, just like the first-phase crafts are still there today. As long as you have the mats, you can still craft the turn-ins for the achievements and turn them in at your leisure. They won't be worth a damn, but they will still count towards the achievement.