"strove to attain" is correct and usable in written English.
It is a verb phrase, in the past tense form of "strive", and it can be used to indicate that someone tried to get something or reach a goal. For example, "She strove to attain the highest honors in her field of study."
Many of the world's leaders and their supporters knew only too well what they wanted, and strove to attain it.
MR. COUNSELLOR SMIRNOV: Then do I understand you k say that this Paragraph 3 was an ideal which you strove to attain but which you were never able to attain?
MR. COUNSELLOR SMIRNOV: I asked you a question; does this mean that the statement can be interpreted as follows: Paragraph 3 of this decree was an ideal which you persistently strove to attain, which you openly professed, but which you were never able to attain?
And they strive to attain the rank of life master.
The new machine would be built for the ideal tritium mixture, but it would no longer strive to attain ignition.
He strives to attain mysticism in choreography that is fraught with a pull between restraint and anxiety.
It will have clear statutory responsibility, it will strive to attain stature and authority, and it will seek to earn respect through effective and appropriate contribution.
On the whole, his lordship prophesied, "the more time he has to devote to his hobby, the more Rugbyman will strive to attain greater efficiency".
The efficiency and professionalism with which my case was handled lived up to high standards that I strive to attain for my own patients.
Consistency is an ingredient managers strive to attain, and Mike Scioscia, in only his third year as the Angels' manager, has molded a model of consistency.
You spend your life struggling and striving to attain this dream of playing in the N.F.L., and then you're out and it's jarring.
