'tremendously vast' is a correct and usable phrase in written English.
You can use it when you want to emphasize that something is very large in size or in scope. For example, "The Amazon rainforest is a tremendously vast ecosystem."
A four-engined aircraft piloted by Sigizmund Aleksandrovich Levanevsky disappeared in the Arctic Ocean and set in motion a large-scale, though unsuccessful, search that covered vast areas hitherto unexplored and added tremendously to flying experience.
"He has obtained Uefa coaching qualifications and will be tremendously respected by the players because of his vast experience as a player.
Insiders, however, are generally convinced that what we do now matters tremendously, because the difference between the best- and worst-case scenarios is vast, and the future is not yet written.
On the show, Betty often gives the other actors constructive feedback and advice based on her vast experience working in the industry, which the cast appreciates tremendously.
"His vast experience and expertise in the tech industry has helped Kander tremendously.
The vast amount of high-throughput data generated by ENCODE has provided tremendously valuable resources but we realized that the numbers of YY1-binding loci provided in original ENCODE datasets are large.
In the economic realm, while standards of living have improved for the vast majority of Chinese, and the country's middle class has expanded tremendously, there is nonetheless a widespread belief that not everyone is enjoying their fair share.
From a social standpoint, the vast majority of these cuts are going to the wealthiest people, who have already prospered tremendously in the last decade.
Although the vast majority of papers published in this area currently are European or North American based, there are tremendously important cultural artefacts found in all parts of the world.
We look tremendously foolish to the rest of the world when we try to dictate how other countries should behave, considering the vast number of critical problems the U.S. faces internally.
