Alistar literally cannot be killed if he has full build in ARAM...

I finished an ARAM match as Alistar and holy shit, he's one tough cow. finished with a score of 6/5/34 (we won).

All you need to build is Guardian's Horn (works like a charm when used in synergy with Unbreakable Will), Spirit Visage + Warmogs for huge amounts of health and 2 more tank items of your choice. I chose Face of the Mountain and was about to finish my build with Sunfire Cape for extra health, and AoE damage.