you have to buy cooldown boots when playing against alistar early on. it allows you to stunlock him or poke him and then outrun his W and Q's range. he's a slow and large champion with literally only 2 strategies that are available for initiation and one requires flash.
morgana is a pretty good answer because her Q has long range and snares and her E is a spell shield. lux is also a good choice.
the main thing though is buy those boots early.
if you want to use soraka then you'll need to start with amulet coin for the extra 5% cooldown. you can also get the free 5% cdr from masteries if you build windspeakers blessing. start with Q and then go E instead of W. try to catch him in the E as much as possible but dont level it up. instead start leveling your W up and just combo your level 1 E and Q to save mana until you have enough gold for your tier 2 income item, the sightstone if you buy it, and those boots. choose when to back meticulously because you'll need to get amulet coins upgrade asap for full benefit. unlike the green and blue income item there is no additional benefit to maxing out the yellow income item as far as gold is concerned.
finally - remember that alistar is a tank so his counters for the most part involve just avoiding him or preventing him from moving. you dont have to kill someone to prevent them from being effective.
. I'm really good at playing her extremely aggressively and I use a great build. I can even zone 
and 
. The only champions that can deal with me consistently are 
and 
. Blitz always gets banned because he's blitz, but nobody really bans Ali. Alistar can literally just insta-murder me because as soon as he gets his combo in, I can't even flash out if the adc is even half-decent.
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