by any means NECESSARY

at ALL costs

I think all that is about probability, at least, it sounds more like someone's attempt to predict a future scenario. Would it then be best to use MAY rather than CAN?

I didn't use 'may' because I thought this could sound like permission/advice.

Uly, in this context 'любой ценой' seems to have negative meaning, i.e. by bad means too, not just by good means. Would be 'necessary' appropriate in this scenario? BTW, that's why I didn't use 'achieve'.

ALL corrected.

Добиваться любой ценой wich always has a negative connotation and “permission"? Грамблер, Вы противоречите сами себе.)

Вообще говоря, я бы не сказал.
Мне наплевать, как ты этого добьешься, но что б оценки было хорошие!
- Я слегка утрировал.

И я бы не сказал always. Вовсе не всегда.

Would 'necessary' be - работа над ошибками

Grumbler, (1) in this context, MAY is the only option. The context usually makes clear whether it’s permission or otherwise - a native will know right away. (2) Especially if this person will stop at nothing to get what he wants, ANY MEANS NECESSARY is the correct phrase.

OK, thank you both. Corrected.

👍🏼