Many companies they have researched on are short of talents.

他们调查的许多公司都缺乏人才。

be short of 缺乏。

例如：The trouble is that we are short of financial support. 问题是，我们缺乏资金支持。

... off ering good career chances is the key to attracting and keeping the talent.

......提供优厚的事业发展前景是吸引和留住人才的关键。

the key to ... （某事成功的）关键；to后面跟名词或动名词。

例如：Transportation has always been the key to developing trade.

交通运输一直是发展贸易的关键。

Yet not every employee feels that they can better their career chances.

但并不是每位员工都觉得他们能够获得更好的事业发展机会。

yet在句中用作并列连词，意思是“然而，可是”。

例如：He studied hard, yet he failed. 他努力学习，可是考试仍未及格。

better 在这里是动词，意为“使......更好；提升。

例如：The government hopes to better the conditions of workers. 政府希望改善工人的条件。

...despite a recent fall in unemployment ...

......虽然近期失业率有所下降......

despite不管，尽管；介词，后接名词性成分，如名词、动名词、名词性从句等，用来表示转折。

例如：Despite his lack of experience, he got the job. 尽管缺乏经验，他还是得到了这份工作。

We're still in the hardest living standards squeeze for over a century and those who are already working have had years of real-terms pay cuts.

一个多世纪以来，我们的生活水平一直处于最艰难的状况，而且，员工的收入多年来实际一直在减少。

squeeze在此处是名词，意为“（可获得的钱、工作岗位等的）减少，削减；拮据，经济困难”。

例如：She has just lost her job, so they are really feeling the squeeze.她刚失业，这下他们真正感到艰难了。