1 That is THE hardest I've ever pushed myself at work.
2 This is the BIGGEST challenge of the day.
3 Could you survive in the hottest place IN the world?
4 Building a shelter was the MOST difficult thing we did.
5 Lara is THE BEST in the class at coping with new situation.
6 Simon is the most experienced person IN our office.
7 My sister is the bravest person IN our family.
8 That course was the WORST experience of my life.

1 the hardest - надо артикль, так как это превосх. степень прилагательного
2 the most big - неверно! Надо: the biggest
3 вместо could - надо Would you be able to survive...,так как could в будущем времени не употребляется, вместо него ставим эквивалент to be able to
4 the more заменяем на the most (превосходная степень )
5 неверно the most good, а надо: the best в превосходной степени
6 of заменим на in
7 at заменим на in
8 the bad заменим на the worst - превосходную степень от сущ. плохой