The English phrase "critical journalism" is most often used to mean journalism critical of some specific person, government, system etc. - in contexts where the object of the criticism is known, whether because it has been explicitly named or not.
For instance: a text about "journalism critical of Donald Trump" may refer to that kind of journalism as "critical journalism" after the first sentence or so.
Or "The XY government is strengthening its assault on critical journalism": here, "critical journalism" almost certainly means journalism critical of the government. It may also connote that it is journalism that is kritisch in the sense that it is clear-eyed analytical journalism - but I think that is more due to the fact that people assume that those things tend to go together in countries that crack down on press freedom than to the meaning of the English term "critical".
I also come across the term "critical journalism" in discussions of balance in journalism. Here too, it means journalism that subjects something to criticism, but in that context the object of the criticism need not be clear, because the point is that, in such contexts, "critical journalism" is journalism does not seek to ensure balance, that "every alpha who expresses an opinion in a piece is paired with a corresponding omega" (from the article at politico.com).
I think I have occasionally seen "critical journalism" used in a sense where "critical" was meant to be understood in its meaning of "exercising or involving careful judgment or judicious evaluation", as in "critical inquiry", "critical analysis", "through a critical lens". But if I were going to do use it that way I would want to make sure that the context made it completely clear that that is what I meant, i.e. at the first use I might write " journalism that is critical in the sense that it is based on an unbiased analysis of..."
BTW I am not sure that kritische Journalismus is the same thing as investigative journalism. I tend to think of investigative journalism as journalism that involves a substantial amount of research to uncover facts that have been concealed, usually (though not necessarily) deliberately, and analyses them.
Imagine a newspaper article summarising a recent national court decision touching on some fundamental right, describing the impacts the decision is likely to have and then detailing objections to the decision raised by legal scholars specialising in the area or describing how court rulings in similar cases in other countries have differed and what conclusions one might draw from those differences.
I would not consider that investigative jouralism, but if it struck me as an unbiased, fact-based and thoughtful piece of journalism, I would have (perhaps erroneously?) considered it kritische Journalismus .