I actually think I have a pretty good answer!
Sky(Skyward Sword Link)(The Hero of the Sky) would be the type of drunk who when drinking is either tipsy, blackout passed out drunk, or that 2nd level of drunk but hasn't passed out yet. He would be a very lightweight drunk, and tipsy for him would be either one or two drinks with very low almost no alcohol content or one decent sized drink with an average/decent amount of alcohol content. The next morning when he's hung over he would be throwing up like crazy and feel super gross, and want to d!e, but would after a while might have some alcohol again.
Time(The Hero of Time) would be about as able to hang as one of my parents. He wouldn't really drink and when he would he would probably only have like one or two drinks before going to bed. He likely would get really really bad anxiety/depression/etc. if he drunk alcohol, and if he drunk enough would probably in his drunkness hallucinate some of his traumas before passing out in a puddle of his own puke and tears for his wife to find, but it's not his fault because he's extra traumatized.
The Hero of Twilight(TP Link) is a farm boy, so he probably wouldn't really drink unless he was going out to a bar with his friends to hangout or on special occasions. He likely would mainly drink beer, whiskey, and tequila because that's the vibes he gives me. In a circumstance he consumed any alcohol while as a dog, even if he wasn't drunk as a result whether he turned back into a human or not he would be super sick and throwing up and wanting to unalive for days. But In normal circumstances, generic sh!tty hangover.
The Link from Hyrule Warriors probably doesn't drink very much, but will have a drink or two of he's celebrating something with his friends. He wants everyone to think he's like this dark, gritty guy who likes really strong alcohols with a sort of kick to them, when in reality he likes his fruity little drinks and cocktails with the sparkling water and strawberries and vodka. This is because he himself is probably a fruit.
The Link from AoC, BotW, and TotK would be almost impossible to get drunk. Either you would need godly liquor of some sort of you would have to make sure he drunk a lot of alcohol with or without water breaks in a very short amount of time, even more alcohol in said short amount of time if he does take water breaks. He would like all alcohols, or at the very least would drink all of them. When drunk, depending on his mood and what type of day hes having and how tired he is, how drunk he is, etc, he could be anywhere from super flirty and seductive to an absolute train wreck to aggressive and violent to just really tired. He would probably get over hangovers quickly, and they wouldn't be nearly as bad. Unfortunately, to many people he looks way to young to be drinking alcohol, so he would learn how to make all the alcohols and always have the ingredients to make the alcohols on him at all times. I know this because you can make a Noble Pursuit in TotK(and probably also in BotW and maybe in AoC but I don't think so for that last one).
Thank you for coming to my Ted talk, good night.