The phrase "achieved a greater" is correct and usable in written English.
It can be used when discussing accomplishments or improvements in comparison to previous efforts or standards.
Example: "The team achieved a greater level of efficiency this quarter than in the last."
Alternatives: "reached a higher" or "attained a larger".
"But here we've achieved a greater bandwidth of spaces on a regular grid".
Blears concluded confidently: "In this report we have achieved a greater transparency than ever before.
We've pursued — and largely achieved — a greater degree of genuine civil liberty than any other nation on earth.
The "highs" also, in most cases, achieved a greater percentage of their improvement goals than did their "low" counterparts.
The actors in "Saved" were initially nervous about him, he said, but seemed to have achieved a greater rapport with him than their British counterparts.
This meant the British singer achieved a greater haul of Grammys on the night than Pharrell Williams and Beyonce, who both left with three gongs.
The phenology-guided composite image from the MSAC model achieved a greater saltcedar mapping accuracy than any single Landsat image in 2004.
Compared with the untransformed control, we achieved a greater accumulation of Sal B (up to 3-fold higher) along with a reduced lignin concentration.
Secondly, and more importantly, therapeutic use of AAV-IL-22, administered after the onset of disease, achieved a greater hurdle and significantly improved portal pathology.
The new, solid, durable glass gradually achieved a greater market than the more fragile Venetian type, and new techniques, more suitable to the new glass, began to replace methods developed for Venetian glass.
A higher virus titer (1 × 1012 viral genomes/animal) introduced through back-table portal vein perfusion and a longer preservation time (3 hours) achieved a greater level of transgene expression until day 180.
