First to say just in case: That sentence is from Tatoeba. All the data on Jisho.org is sourced from different places and always attributed. In this case you can go directly to the source (for example to get more detailed info, or to contribute an edit): https://tatoeba.org/ja/sentences/show/170563
In the case of this sentence, the source doesn't give much more info, the only interesting tidbit is that it is tagged with "Tanaka Corpus". This means that this example sentence, before it got moved over to the Tatoeba project, used to be part of the somewhat (in)famous Tanaka Corpus. You can read more about that here: http://www.edrdg.org/wiki/index.php/Tanaka_Corpus As you can see from there, that project never really had a high quality-standard, as it was pretty much just a homework task done by Japanese university students. Of course, over the last 20 years people have improved upon the original work, but... not every example sentence pair is completely ideal to maybe put it like that.
Not every example sentence here on Jisho.org is like that. There are some from the Tatoeba project that haven't had their origin in the Tanaka Corpus, and then there are also some sentences from the Jreibun project. The latter in particular has the aim to provide high-quality sentences suitable for language learners. That's why in general these are shown preferably by Jisho.org if you search for something like https://jisho.org/search/最後%20%23sentences (The first page of search results has all sentences from Jreibun)
To comment on this specific sentence: 詰め（つめ） is the final, last stage of something, some kind of process. Originally comes from 将棋（しょうぎ）, the chess-like Japanese board game. Without any context, you could more or less end up with what Google makes of it here.
The pronunciation: 最後 の 詰め（つめ） に 入る（はいる） とき です。
つめ is indeed 詰め here. In a certain context, the final thing that has to be done might be killing a specific person/animal or whatever. That could be a reason for why it was translated this way. But I don't know. 詰め（の段階）に入る can be used in many contexts.
"to go in for the kill" is an idiom in English meaning "to finish something up"
so there is no difference between the given translation and what google suggested you
最後のつめにはいるときです。inquiry word by word?
The translation reads: It's time to move in for the kill. Google translate reads: It's time to reach the final stage. These translations seem different to me. Then who introduced this sentence? And could you please elaborate word by word?
Or is it a figure of speech common for japanese people to use? If so, in what situations would they use it? Sports? Exams? Combat? Bushido? Maybe a lead singer saying this to his fellow band members before returning to the stage to perform their last song at a concert?
How should I pronounce this sentence?
saigo no tsume ni hairu (入る) toki desu OR saigo no tsume niwa iru (にはいる) toki desu ?
The word つめ in this sentence ; does it stand for 詰め (final stage / endgame)?
Or does it sort of stand for ‘the kill’? Like: Let’s enter for the final kill? Can I use this sentence in combat or bushido?