Back in the days when Jaime Lannister still had his preferred right hand, the oath-breaking sister-lover was easily one of the most formidable warriors in Westeros. Though - as far as we know - he has never ventured further north than Winterfell and may not even believe in the supernatural beasts that live beyond The Wall. Still, based on what we saw in The Watchers on The Wall we have to say that Tywin Lannisters eldest son would be capable of dispatching a Giant. His prowess on the battlefield may have just been proven against the more conventional warriors of Westeros but it's hard to deny that the incredible skill of the Kingslayer couldnt be used to pick a Giant apart. In the most recent episode we saw the aftermath of the encounter between Grenn et al and one of the lumbering beasts; perhaps surprisingly, the Nights Watchmen had been able to fell the brute (dying in the process). Somewhat primitive fight-mathematics state that Jaime would easily be able to handle this small squadron of the Nights Watch and by extension should be able to overcome a Giant. While it doesnt always work like this, we have to say that the legendary fighting ability of Jaime with a sword should allow him to bring down a Giant.