This involves inversion (倒裝) in classical Chinese. The most sensible arrangement in modern Chinese is
To go towards / approach (sth.) with all one's might,
which obviously suggests the meaning 'trying one's best in doing something'. The grammatical object is the target but is omitted (perhaps understood) in the idiom.
While 赴 is transitive, 全力以赴 ...
people or generations to adapt to the given situation or environment
People who live near mountains make a living in the mountains, people who live near the sea make a living in the sea
Notice: 靠 here doesn't mean depend on. It means lean against = near; close to
根據環境的實際情況制定相應的辦法 - Formulate corresponding measures according to the actual ...
A lot of Japanese 四字熟語 and Chinese 成语 have the same form and meaning. Both inherit from classical Chinese literature. Examples: 一衣帯水（いちいたいすい） , 異曲同工（いきょうくどうこう）
Some have a slightly different form and basically the same meaning. Example: Japanese: 一心協力（いっしんきょうりょく）, Chinese: 同心协力
Some have the same form but different meanings. Examples: 一刀両断 In Chinese it ...
I recommend 多功能成语词典 which is available as a (not free) add on to Pleco. It gives this explanation for 全力以赴:
This makes it clear that 赴 in 全力以赴 carries the idea of movement / signifies "to go".
(I think L Parker's answer is the best so far, but hopefully this comment still is worth putting up as an answer as it has a ...
打采 -- 意思是指狎客给妓女的缠头, (it refers to the headdress / headwrap, (缠头), of prostitutes in ancient China)
Please Note -- my interpretation #1:-
Prostitutes, or women in general, ancient or modern, take great care / attention with their hair which ensures good looks or at least presentability. Something of importance and a daily necessity, especially for prostitutes ...
Looking for logic in language? Likely an long look!
Why is it called 赴 fù when it is composed of zǒu and bo or bǔ?
zdic.net has this for 赴：
2 投入（某种境地），参加（某种行列）：赴战。赴敌（加入对敌作战）。赴难（nàn ）。赴义。
全力以赴：throw oneself into the fray with all ones might
Usually you can use any of them, but "攻其无备，出其不意" is the best one.
The reason is this word is from 《孙子兵法》, an ancient military book by a famous military strategist Sun Wu(孙武), and it is "攻其无备，出其不意" originally in that book.
Also, in 《现代汉语词典》（第7版）, there is "攻其无备，出其不意" under "出其不意" as an example.
First of all, 高 doesn't only mean high or tall. 高 also figuratively means good, smart, superior and so on. E.g. 高招 (smart move), 高人 (a person who has very good idea).
so, 高人一等，literally means 比别人高一个等级，which figuratively means better than/superior to other people.
It can be used both positive and negative ways. When you describe quality, strategy, and so on, ...
According to here https://idiom.wlps.kl.edu.tw/dict_idioms/448.html
there are multiple variants of this word:
兩短三長, 一長半短, 一長兩短, and 三長四短 etc.
長 and 短 could mean some change while 三, 兩 or other numbers may be used to express that the amount of change is random and unpredictable. Based on my experience this word is often used to suggest the possibility of ...