to remain firm in your beliefs or decisions despite opposition
оставаться твердым в своих убеждениях или решениях, несмотря на сопротивление (ostavat'sya tverdym v svoikh ubezhdeniyakh ili resheniyakh, nesmotrya na soprotivlenie)
"Even though they disagreed, he decided to stand his ground and not back down."
"Хотя они не согласились, он решил стоять на своем и не отступать." (Khotya oni ne soglasilis', on reshil **stoyat' na svoem** i ne otstupat'.)
to succeed in doing something difficult
someone new to a place or situation
to do something as fast as possible because time is limited
to establish an example of excellence that others strive to...
to laugh uncontrollably
a situation has started to change in your favor