Is becoming a Master an achievable goal?

I think it is achievable for most players under age 30 who start putting in 3-4 hrs/day. I coached a high school chess club and I had players who put in about 1-2 hr/day who became top-10-in-county (1300+ rating) and were weak academically and behind avg. in math as well as those who were gifted academically. I think any of them could have reached master with 3-4 hrs/day and proper coaching, though obviously the gifted teens were more numerous in that group and probably more likely to progress because of their already-developed self-discipline and study habits.
I also was USCF Tournament Director for my county's scholastic, OTB, regular-rating tournaments and parents and coaches from other schools often noted that academic excellence did NOT determine which kids had strong ratings at their schools.
The older you get the more difficult it is to play good chess in less than 90 min. per clock games. All of the people I've heard about who reached OTB regular-rating master in their 50's or later were Class A players or better much earlier in life.
Still, I think it's possible, though not a sure thing, for a 1500's player to get to master level at any age IF they can seriously study for at least 4 hours/day.

I did it but I had smaller goals from the start and didnt really think about becoming a master until I actually beat a few in tournament games . I played my first tourney in 73 at age 20 and lost every game . I first broke 2200 in 1984 , it took me 11 years . My first goal was to be better than one of our club players who was very arrogant and used to beat me mercilessly and then gloat about it , he was only B class in strength but I was just starting . I recall my next goal was to be an A class player . As an A class player I started playing against experts and masters and began to beat some of them . At this point I set 2 goals : to break 2200 and become Ga state champion . I broke 2200 in 84 and then became state champion in 87 . Set reasonable goals and then set new ones as you achieve them .
Possibly of interest:
"... the NM title is an honor that only one percent of USCF members attain. ..." - IM John Donaldson (2015)
http://www.jeremysilman.com/shop/pc/Reaching-the-Top-77p3905.htm
What It Takes to Become a Chess Master by Andrew Soltis
"... going from good at tactics to great at tactics ... doesn't translate into much greater strength. ... You need a relatively good memory to reach average strength. But a much better memory isn't going to make you a master. ... there's a powerful law of diminishing returns in chess calculation, ... Your rating may have been steadily rising when suddenly it stops. ... One explanation for the wall is that most players got to where they are by learning how to not lose. ... Mastering chess ... requires a new set of skills and traits. ... Many of these attributes are kinds of know-how, such as understanding when to change the pawn structure or what a positionally won game looks like and how to deal with it. Some are habits, like always looking for targets. Others are refined senses, like recognizing a critical middlegame moment or feeling when time is on your side and when it isn't. ..." - GM Andrew Soltis (2012)
https://web.archive.org/web/20140708093409/http://www.chesscafe.com/text/review857.pdf
100 Chess Master Trade Secrets by Andrew Soltis
https://web.archive.org/web/20140708094523/http://www.chesscafe.com/text/review916.pdf
http://dev.jeremysilman.com/shop/pc/100-Master-Trade-Secrets-77p3835.htm
Reaching the Top?! by Peter Kurzdorfer
"... On the one hand, your play needs to be purposeful much of the time; the ability to navigate through many different types of positions needs to be yours; your ability to calculate variations and find candidate moves needs to be present in at least an embryonic stage. On the other hand, it will be heart-warming and perhaps inspiring to realize that you do not need to give up blunders or misconceptions or a poor memory or sloppy calculating habits; that you do not need to know all the latest opening variations, or even know what they are called. You do not have to memorize hundreds of endgame positions or instantly recognize the proper procedure in a variety of pawn structures.
[To play at a master level consistently] is not an easy task, to be sure ..., but it is a possible one. ..." - NM Peter Kurzdorfer (2015)
http://www.thechessmind.net/blog/2015/11/16/book-notice-kurzdorfers-reaching-the-top.html
http://www.jeremysilman.com/shop/pc/Reaching-the-Top-77p3905.htm

I did it but I had smaller goals from the start and didnt really think about becoming a master until I actually beat a few in tournament games . I played my first tourney in 73 at age 20 and lost every game . I first broke 2200 in 1984 , it took me 11 years . My first goal was to be better than one of our club players who was very arrogant and used to beat me mercilessly and then gloat about it , he was only B class in strength but I was just starting . I recall my next goal was to be an A class player . As an A class player I started playing against experts and masters and began to beat some of them . At this point I set 2 goals : to break 2200 and become Ga state champion . I broke 2200 in 84 and then became state champion in 87 . Set reasonable goals and then set new ones as you achieve them .
I think Reb's approach is solid. Set mini-goals, work hard to reach them, then move up the ladder to the next mini-goal.
Well done, Reb!!

Short-term goals are the best thing to improve, not only to get a title, but to improve objectively in chess. Little by little, homie.
... if de la Maza's experience shows us anything, it is that you can reach 2000 simply by practicing tactics until you are blue in the face.
http://www.chess.com/article/view/the-michael-de-la-maza-story
Apparently, he had "studied openings, endgames, and other 'chess knowledge' information."
... The point was ... that it is possible to become a strong class A by studying tactics almost exclusively (and @kindaspongey, ... [de la Maza] started studying openings and strategy and did not improve. It was not until after he was told his weakness was tactics - as it is with virtually every player below 2000 - that he dedicated his time to studying them). ...
That does indeed indicate that he needed to work on tactics, but I do not see how it shows "that you can reach 2000 simply by practicing tactics until you are blue in the face." Apparently, he had "studied openings, endgames, and other 'chess knowledge' information."
http://www.chess.com/article/view/the-michael-de-la-maza-story
... You are stopping halfway through the first paragraph of the story ...
That is incorrect. http://www.chess.com/article/view/the-michael-de-la-maza-story
... If you read the very next sentence after what you quoted, you will see a very enlightening piece of information.
There is this sentence: "Like many adults, he assumed that he needed to augment his natural skills and intelligence by compiling chess knowledge: he studied openings, endgames, and other 'chess knowledge' information."
The very next sentence is: "Despite all that accumulation of knowledge, he was getting nowhere."
Again, that (along with the subsequent stuff) does indeed indicate that de la Maza needed to work on tactics, but I do not see how it shows "that you can reach 2000 simply by practicing tactics until you are blue in the face."
http://www.chess.com/article/view/the-michael-de-la-maza-story

I did it but I had smaller goals from the start and didnt really think about becoming a master until I actually beat a few in tournament games . I played my first tourney in 73 at age 20 and lost every game . I first broke 2200 in 1984 , it took me 11 years . My first goal was to be better than one of our club players who was very arrogant and used to beat me mercilessly and then gloat about it , he was only B class in strength but I was just starting . I recall my next goal was to be an A class player . As an A class player I started playing against experts and masters and began to beat some of them . At this point I set 2 goals : to break 2200 and become Ga state champion . I broke 2200 in 84 and then became state champion in 87 . Set reasonable goals and then set new ones as you achieve them .
Great advice! Set small achievable goals in front of you and achieve them. I have been playing for 5 years now I feel like I'm hitting a brick wall. I have recently joined a chess club and I'm learning again. Playing OTB is a whole different game. I am just starting to enter competitions now. My next goal is to win a local competition and then when my rating goes up win one at the higher level. It's too far ahead to say can I become a Master. Maybe it's too far ahead for the OP to view it like that. But step by step, goal by goal maybe it's possible..........
... "So it turned out HTRYC was not the panacea that Michael [de la Maza] had hoped. But what was? So, in desperation, Michael turned to some other fundamental (and common sense) advice about learning tactics really well, and augmenting other analytical skills. For example, he developed and performed a series of very intense "board vision" puzzles to improve his ability to quickly and accurately determine what was happening on a chess board. While not giving up tournament play, Michael did, for a short time, essentially "lock himself in a closet" and intensely work on some specialized basics." ...
Again, that does indeed suggest that he needed to work on tactics, but I do not see how it shows "that you can reach 2000 simply by practicing tactics until you are blue in the face." Apparently, he had "studied openings, endgames, and other 'chess knowledge' information."
http://www.chess.com/article/view/the-michael-de-la-maza-story

Yeah, mostly you have to enjoy playing and learning about chess. If you play and learn every day, after some years you'll have improved a lot. Whether or not you improve enough to make master depends on your motivation and, ok, at least partly on your age.
But anyway, the stuff you ask about goals and titles doesn't really matter. Mostly you need to enjoy playing and learning.