If you're trying to all in lane opponents, you're doing it wrong. Galio is a poke champ who excels at wave clearing early on and harassing opponents while soaking damage with his high MR. You should take scaling MR glyphs instead of scaling AP, because he gets free AP from the MR anyway while being much tankier for it. Rush Chalice into Abyssal scepter almost every game, and then build whatever AP/MR items suits you and the current match, usually focusing on MR and getting void staff and Rabadon's for max damage. For your armor item, I'd actually skip Zhonya's (now that it has been nerfed, it isn't a must buy on mages) and get a Thornmail. Thorn mail makes your ult hurt a ton (since everyone is AAing you anyway) while keeping you safer during the channel by reducing the damage you take on top of your shield's armor.
I'd recommend a build that looks like this:
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(merc treads and Sorc shoes are a toss up depending on how much CC and MR the enemy team has. Low CC? buy sorc shoes. High CC? buy Merc treads and still do a lot of damage)
also, remember to shield up before casting your full combo, since your shield gives up to 45 free AP just for being on you.
Galio is definitely a counter pick champion, and does really well against AP champs (obviously), but also quite well against teams that are low in AA damage (although thornmail does patch up that weakness).