I don't remember ever making an effort in which I gave something my absolute best.
I don't have any memory of working so hard at something that I thought I would die from it.
ご質問ありがとうございます。
① "I don't remember ever making an effort"＝「努力をしたことを思い出せない」
"in which I gave something my absolute best."＝「何かに対して最善を尽くしたことを。」
② "I don't have any memory of working so hard at something"＝「何かに頑張った記憶がない」
"that I thought I would die from it."＝「死ぬかと思うほどの。」
ご参考に。
アメリカ合衆国 
