приложить все усилия

do one's level best; do one's possible; do one's utmost; give the best sb. has in the shop; take much trouble; go out of one's way to (while we went out of our way to ensure clients were aware of these risks, we now believe them to be marginal Olga Okuneva); put out all one's strength; make every attempt (TranslationHelp); use its best efforts (reverso.net kee46); exert every effort; strain every nerve; do possible; do one's damnedest (Anglophile); bend every effort (к тому, чтобы... – to... Anglophile); exert all powers; ensure (typist)

Игорь Миг

make every possible effort (РФС намерен приложить все усилия, чтобы установить личности и наказать болельщиков, выкрикивавших оскорбления в адрес капитана сборной России Артема Дзюбы в матче против команды Сан-Марино)

amer.

give the best one has in the shop (Bobrovska)

brit.

do as best you can (ad_notam)

cliche.

try one's best (igisheva)

formal

make every effort ("We should certainly make every effort to avoid scandal in so delicate a matter." (Sir Arthur Conan Doyle) ART Vancouver)

idiom.

leave no stone unturned (Ivan Pisarev); go out of one's way (“We’re asking everyone to go out of their way to conserve water to the greatest extent possible, including minimizing lawn watering,” Montgomery said. Other suggested ways to reduce water consumption is taking shorter showers and only doing full loads of laundry.

nsnews.com ART Vancouver); pull out all the stops (для достижения цели Taras); fight tooth and nail (I'm going to fight tooth and nail for that promotion. Val_Ships)

inf.

go to great lengths (people usually go to gteat llengths to make sure thay are not caught Val_Ships); go to the bitter end (to do something Tamerlane)

law

exercise best efforts (elena.kazan)

Makarov.

bear down; move heaven and earth; spare no effort; take all sorts of pains

have pulled out all the stops (to + inf. ... – ... для того, чтобы + инф.; CNN Alex_Odeychuk)

subl.

do one's best (Soulbringer)