1.) The first word in the characters of 一心不乱 may be partially seen in the background on the wall scroll. Personally spoken, it is one of those beautiful, but simple words that carry the spirit of Japan.
一心不乱 (いっしんふらん) = with heart and soul, wholeheartedly, with undivided concentration
i.e. 二人は一心不乱に練習 （れんしゅう） を夕方（ゆうがた）までし続けた。
2.) Another such word is 切磋琢磨 (せっさたくま, to cultivate one’s character by studying/working hard). If added a suffix し合う, it becomes the following expression:
切磋琢磨し合う (せっさたくましあう) = to work hard together or to improve by friendly rivalry
3.) The next is an idiomatic expression, deriving allegedly from an utterance of Tokugawa Ieyasu (徳川家康) after the successful battle of Sekigahara. Many years before this decisive battle was fought, his then overlord was killed in a surprise assault while holding a victory ceremony.
勝って兜の緒を締めよ（かってかぶとのおをしめよ）= after a victory tighten the cords of your helmet / don’t let your guard down even after a victory
4.) Lastly an alternative expression of がんばります (to do/give one’s best). This phrase is more formal and works therefore also towards people of higher status (i.e. workplace) when cheering for them and wishing them success for an upcoming task.
健闘 (けんとう) = fighting bravely, strenuous effort / good luck
・ ご健闘を祈ります (regular -masu form)
・ ご健闘をお祈りします (formal)
・ ご健闘をお祈り申し上げます (most formal way of addressing)