The phrase "achieved their final" is grammatically correct and can be used in written English.
It can be used in contexts where you are discussing the completion of a goal or milestone, often in relation to a process or journey.
Example: "After years of hard work and dedication, the team achieved their final objective in the project."
Alternatives: "reached their ultimate" or "attained their last".
Later they reverted briefly to the Spanish crown, and they achieved their final independence in 1865.
To-day the Red Army [Republican forces] is captive and disarmed, and the Nationalist troops have achieved their final military objectives.
From January 2014 onward, the three spacecrafts were maneuvered apart and achieved their final constellation on April 17 , 2014
All other surveys in Table 2 were carried out once the first cleaning of the Padrón resulting from the 'expiry procedure' for non-EU migrants was fully implemented10, and all of them achieved their final numerical targets by applying an exclusively individual random sampling based on the Padrón.
On 21 September the team achieved their final win of the campaign, beating Southport 2 1 thanks to two goals from Laycock.
The late Burnett Bolloten's monumental book ends with Gen. Franco's final communique of a tragic but inevitable conflict: "Today the Nationalist troops, having captured and disarmed the Red Army, have achieved their final military objective.
In contrast to muscle flaps, which require muscle atrophy over time to achieve their final appearance, there was a similar flap contour from approximately 1 month postoperatively throughout the duration of follow-up.
Membrane-spanning domains of integral membrane proteins must achieve their final folded structure in a very different environment, the hydrophobic interior of a lipid bilayer, compared to that experienced by soluble proteins.
They recognize the context they are in as positive and so they act in a very committed way in order to achieve their final goal.
