I am publishing now just to begin receiving feedback on the build. I will flesh out and pretty up the guide as time goes on. Thank you for your patience.

Update 1/07: I have been trying out a few other builds and have switched some items around from the original builds. Still not final but I appreciate comments. Main intent with changes now is to increase damage potential, especially on the AP side, without reducing AD damage or survivability too much. I am also trying to fit in more MR but MR items just aren't as strong as armor items for damage potential. Suggestions appreciated.

Really wish Lich Bane and Triforce stacked.

I've spent a bit of time looking around for champions that can reliable carry a game in solo queue. To do so, I needed a few things on my champion:

AD/AP scaling:
After playing a few Tryndamere games, it became clear that doing only AD or AP makes counter building far to easy.

Death avoidance:
It is important to be able to stay alive to deal hybrid damage. There's a few ways to do this, such as massive lifesteal (Sion, Ryze), immunity (Kayle, Poppy, Tryndamere), or extreme tankyness (Alistar, Mundo, Rammus).

Crowd Control:
It is also important to be able to control the enemy team, both with movement prevention to secure kills and gap closers to aid in correct position to avoid enemy crowd control. Hard CC is prefered to soft cc (stuns vs slows, silences, etc) with knock-ups being the best because they aren't subject to tenacity.

Adaptability:
I also hoped to find a champion that could perform in solo or duo lane, or even in the jungle, though the expectation in this guide is you to go solo top to farm for long enough to get Trinity and start wrecking faces. Jungling on Alistar is interesting but very much possible, and of course his bot lane is amazing.

Overall, Alistar outperforms any other champion I've tried for hardline 1v5 carrying at low to midrange elo.

I use either magic pen or armor pen depending on what it looks like my team will be more lacking. I get quints and marks here.

I use flat armor seals so I can counterjungle and clear camps if my jungler is otherwise engaged. This helps farm up Trin faster. Scaling armor or dodge would also work as well, though ideally there should be some physical damage reduction.

I use scaling MR glyphs because I need more MR late game. Magic damage is a weakness of this guide, with reliance on its burst being insufficient for a kill with the only real threat being auto-attackers. If magic damage is stacked on the other team, it might be a good idea to sub in more MR runes and modify the build.

With the mastery change, I have switched to defensive masteries for CC reduction and flat HP. Experimenting with Ruby Crystal start I can now usually just outright kill someone by level 3 which helps get my GP5s faster to get snowballing. Late game CC reduction is just worth far more than anything else. I also like death timer reduction, but everything else can change on a game to game basis or personal choice.

I vary my start depending on my laning opponent and lane.

For jungle:
Cloth armor and 5 pots

For top v AD
Cloth armor and 5 pots

For top v AP
Regrowth Pendant and 1 mana pot

For top v AoE dependent champ or against lvl 2 ganking jungler
Boots 3 mana pot

For quick HoG:
Rudy Crystal (also strong for FB)

I blue pill as soon as I can afford philo stone/HoG. I build as many GP5 items as I think is reasonable (sometimes none even, rushing Sheen instead if I'm snowballing) and then build trinity starting with Sheen. Sheen is the strongest component of Trinity for Alistar (and in every AD or AP Alistar build) and naturally is taken first. Often I go straight to Trinity from Sheen if I run 4 GP5s+boots. After Trin I complete my boots but it varies by game and situation. With Trinity, team-fighting is a good idea.

After Trinity Force, I general build full RoA while fulfilling a tank role in order to begin stacking the bonus. The bonus and midgame tankyness are the only reasons it's taken over Atma's or other mitigation items, the AP kicks in later. If you're snowballing and need ad, you'll probably want to take a Atma's. RoA is incredible strong on Alistar.

The next items are largely dependent on incoming damage type, but I'm almost always going Abyssal Scepter next as my MR is sorely lacking. However, if mage burst is all happening while ulted, simply take Frozen Heart (or just Glacial Shroud) next. These two items, built in any order, nicely round out the build.

A word on FoN and FH:
I select Frozen Heart for the permanent aura and CDR, the only reason for its choice over Randuin's. If you prefer Randuin's, take it, but realize it reduces outgoing damage with the CDR loss. However, if the Randuin's active can reliably turn teamfights, it comes highly recommended. Against minimal magic damage, I usually take it over FoN. Thornmail, the only other high armor item, simply lacks stacks. The only other item I would consider is Sunfire Cape, but that has far less armor. Again, it depends on the game.

I take Abyssal Scepter over FoN or BV now because I wanted more AP. FoN is a stronger MR item but a weaker hybrid item.

Overall, I aim for about 4k health, 200 to both resists, and 200+ AD before Nashor/elixirs. Change resists based on the enemy team. I have recently shifted to reducing health in favor of AP and found that both have their uses, but it seems a bit over 3k is sufficient with the slightly strong heal and more burst.

There is no skill sequence! Take what you need!

For solo top I usually max heal to make myself ungankable unless I can get kills on charge.

For jungle I usually max knock up because its an aoe and destroys creeps.

For bot I usually max charge because it protects my lane mate and does the most damage.

For top, teleport is mandatory in case a fight starts bot or at dragon... unless Exhaust will get kills.

In jungle, smite is mandatory because its the freaking jungle.

I highly recommend flash to flash behind people and knock them into your team or turret. It isn't mandory however.

Cleanse is very strong agaisnt high CC teams.

Exhaust is very strong against Tryndamere.

Clairvoyance is nice for juking teams into thinking you're only a support.

Ignite can net early kills and counters Vlad/Mundo.

Ghost doesn't seem that strong to me on Alistar, but it is a reasonable choice.

Rally is awesome for trolling... how I miss it :(

This is a relatively brief guide, moreso a defensive of Alistatmogs (now more like... Rodistar?) or whatever we should call him. I hope you find it helpful. It is the most reliable 1v5 capable build I've managed to come up with, and I would appreciate feedback.