Onu geçtiðinde kaplumbaðanýn  yüzünün alacaðý þekli düþününce,  gülerek uykuya dalmýþ.

My attempt as learner:

When he overtook him, he smiled at the thought of how turtle must be surprised(*) and then fell asleep.

(*) Literally: at the thought of how turtle´s face will look like - I don´t know how to properly translate it to English, but I think it can be replaced with "at the thought of how turtle must be surprised" in this context.

I think the end of the sentence  ´gülerek uykuya dalmýþ´ is ´he fell asleep laughing´

´So maybe it´s

When he thought/thinks  of the way the turtle´s face will be when he passed/passes him,he fell/falls asleep laughing.

My try

Thank you!