The phrase "achieve a modicum of" is correct and usable in written English.
It can be used when referring to obtaining a small or moderate amount of something, often in a context where that amount is considered sufficient or satisfactory.
Example: "After months of hard work, the team was finally able to achieve a modicum of success in their project."
Alternatives: "attain a small degree of" or "gain a minimal amount of".
The Benghazi attacks also crystallised another lesson for US officials: helping Libya achieve a modicum of security was paramount.
Despite its "non-volatility"—a huge advantage over "volatile" chips such as DRAM, which lose their data if not continually refreshed it still took flash a decade to achieve a modicum of success in the marketplace.
Because the US understands and shares this objective, as do many others in the west and the moderate Arab countries, it looks like Israel still has time to achieve a modicum of its objectives.
Similarly, in the mid-1980s OPEC did not cooperate in the face of painfully low prices; only when Saudi Arabia punished the group by flooding the market did it achieve a modicum of coordination.
Malcolm Gladwell has recently popularized the idea that 10,000 hours or 10 years of dogged dedication are required to achieve a modicum of expertise.
This call lay behind Zhu's promotion of the Great Learning (Daxue) and call for life-long learning and moral reflection in a bid to achieve a modicum of objectivity and break free of the moral intuitionism and resultant subjectivism typical of Neo-Confucians of his generation.
You actually cite monetary and trade policies as areas where EU governments have actually achieved a modicum of success.
Despite the years of unpaid bills, it was only once the Kickstarter achieved a modicum of success that developers spoke out.
This flawed structure was also based on the premise, a naïve one at best, that the United States had a national interest in moderating Israeli behavior and achieving a modicum of justice in the Middle East.
