The phrase "achieving most" is not correct and may lead to confusion in written English.
It could be used in contexts where you want to express reaching a high level of success or completion, but it lacks clarity.
Example: "The team is focused on achieving most of their goals by the end of the quarter."
Alternatives: "reaching the majority" or "attaining most".
Should we fault Obama for achieving most of this on the sly?
Cowperwood, like all of Dreiser's major characters, remains unfulfilled despite achieving most of his apparent wishes.
White House officials said the president would make the announcement Wednesday as part of a release of broad principles to overhaul the tax code — days before a 100-day deadline Trump had given himself for achieving most top campaign goals.
Also, she was less prolific than either of them, achieving most of her renown on the strength of her first three solo albums and one soundtrack, released from 1985 to 1992.
I was happy, therefore, when Adolf Hitler, in a most wonderful rise to power, unparalleled in the history of mankind, succeeded by the end of 1938 in achieving most of these aims; and I was equally unhappy when in 1939, to my dismay, I realized more and more that Adolf Hitler appeared to be departing from that course and to be following other methods.
Achieving most goals requires work.
Huge congratulations to Ed Sheeran on achieving most-streamed album on Spotify for the wildly successful X, and also for earning the overall most streamed artist of 2014 thanks to his dedicated fans on Spotify".
The Meliorists achieve most of their seven-point agenda.
Five years ago one could have achieved (most of) this by just trying to watch porn.
Cape Verde is on track to achieve most of the millennium development goals (MDGs) by 2015.
Mr. Clinton himself achieved most of his success by turning these habits into a master strategy.
