Another difficult expedition was (the time) when he tried to walk across Antarctica.

[diamondcutter]

Guinness World Records describes Fiennes as ‘the world’s greatest living explorer’. He has been on more than 30 expeditions. ... Another difficult expedition was when he tried to walk across Antarctica in 1993 with Dr Stroud.
Source: Kid’s Box 6, CUP

Can I paraphrase the last sentence like this?

Another difficult expedition was the time when he tried to walk across Antarctica in 1993 with Dr Stroud.

 

[teechar]

You can, but it doesn't sound as good, because it equates expedition with time. You could use "occasion", I suppose, but I still think the original is the best.

 

[Phaedrus]

Another difficult expedition was when he tried to walk across Antarctica in 1993 with Dr Stroud. [. . .]

Can I paraphrase the last sentence like this?

Another difficult expedition was the time when he tried to walk across Antarctica in 1993 with Dr Stroud.

In a paraphrase, I'd prefer to substitute "was" with "happened," "occurred," or "took place."

Another difficult expedition took place when he tried to walk across Antarctica in 1993 with Dr. Stroud.