Focuses on: Cooldown reduction, Crit chance, and Attack speed.

Crit chance serves as a kind of secondary Cooldown reduction, maximizing the usage of Spinning Slash without sacrificing damage output.

Higher Crit chance=More crits
More crits=More Fury
More Fury=Higher Crit chance

Greater Glyph of Cooldown Reduction working in tandem with Sorcery to ensure 40% CDR at level 18.

*Note: Champ stats at the top of the page do not include CDR gained from Sorcery, which maxes CDR.

Mostly standard AD-based offensive masteries (see Sorcery below), with some questionable defensive masteries.

Sorcery complete's the 10% CDR chunk unfinished by Greater Glyph of Cooldown Reduction, allowing 40% CDR to be reached using only AD/CDR items. Sacrificing the 3% Attack speed bonus from Fury is a small price to pay, relative to the temporary 10% Attack speed bonus from Frenzy that is easily procced at level 1 by Greater Quintessence of Critical Chance, Greater Mark of Critical Chance, Brawler's Gloves, and any existing Fury. (22% Crit chance at level 1, with no Fury. 57% Crit chance at level 1, with full Fury.)

Perseverance can make the difference when suffering minion auto-attacks/DOTS after Undying Rage expires.
Most people prefer Veteran's Scars . I'm a fan of synergy, and Tryndamere synergizes with having low health. I prefer Perseverence .

Tough Skin : For trading hits in lane, chasing through swarms of minions, and escaping after an ult.

Bladed Armor is a modest, single-point investment, considering you could kill a minion with it while trading hits with another champ in lane, granting you 10 Fury.

Notice Tryndamere is bare-foot?
Between Phantom Dancer, Zephyr, Trinity Force, and Spinning Slash being spammed at least once every 2 seconds, he's not worried about movement speed.

Youmuu's Ghostblade: A perfect item for this build. Why?
1: 15% Crit chance... Yeah.
2: 20 Armor penetration... Which the runes are lacking.
3: 10% Cooldown reduction... More spins and, ultimately, more ults.
4: 30 AD... Give me that.
5: Unique active... A 6 second boost of 20% move speed and 40% attack speed, every 45 seconds? Icing on an already delicious death cake.

Phantom Dancer:
1: 30% Crit chance... Always welcome.
2: 50% Attack speed... Still want to trade hits?
3: 5% Movement speed... Then do me a favor and run away.
4: Unique passive (ignore unit collision)... And while you're at it, try not to step on any minion's toes. *Tryndamere proceeds to step on all toes.

Zephyr:
1: 10% Cooldown reduction... More spins? Yeah.
2: Tenacity... 35% less wasted time on a temporarily invincible champion? Yup.
3: 10% Movement speed... No boots? No prob.
4: 50% Attack speed... Faster crits, more spins.
5: 25 AD... If you must add Attack damage to this item, so be it.

Trinity Force:
1: 30 AP & 30 AD... Spinning Slash scales well with both. Not wasted.
2: 30% Attack speed... Faster crits, more spins.
3: 10% Crit chance... Not impressive, but not wasted either.
4: 250 Health... Nice to have, but not important.
5: 200 Mana... A wasted stat that neither makes nor breaks this powerful item. Case in point: Sange & Yasha gave no mana.
6: 8% Movement speed... Running barefoot has never been this good.
7: Unique passive (Icy)... Good for chasing.
8: Unique passive (Spellblade)... Ever since they made this scale with base AD, I felt slighted while using this item. However, spamming Spinning Slash at least once every 2 seconds makes great use of this passive.

Infinity Edge:
1: 25% Crit chance... Moar.
2: Unique passive... +50% Crit damage is incredible. On this build, it might as well say "+50% Auto-attack damage".
3: 70 AD... The highest AD item in this build. I appreciate it.

Black Cleaver:
1: 50 AD... Not bad at all.
2: 10% Cooldown reduction... Another puzzle piece of perfect CDR.
3: 10 Armor pen... Lacking in runes, welcome here.
4: "Dealing physical damage to an enemy champion reduces their armor by 5% for 4 seconds. This effect stacks up to 5 times."... Spinning Slash procs this passive.
5: 200 Health... If you must...
Overall, similar yet superior to Last Whisper, considering the other benefits of this item, particularly the CDR.
Black Cleaver is last in the item build, because % Armor pen increases in effectiveness against higher armor values, and I'm a fan of synergy.

Spinning Slash is maxed first for a few reasons.

1: Unlike Bloodlust, Spinning Slash's cooldown is reduced with every level. In addition to dealing damage, this ability repositions Tryndamere, making it possible to attack in certain situations where, otherwise, a longer cooldown would leave you out of range.
2: Despite Bloodlust's AD increase, maxing Spinning Slash first increases damage output more with this kit, as it is very spammable.

Ghost and Exhaust help you stick to your targets. Give Tryndamere credit for dealing lots of damage when he's in range, keep it that way.

Ghost ultimately covers more ground than Flash, and besides: Tryndamere can spin through walls.

Because Tryndamere's kit deals so much damage itself, I would prefer Exhaust over Ignite not just because Tryndamere will get more attacks in while chasing, but also because with the Summoner's Wrath mastery, the reduced armor will magnify Tryndamere's damage output, whereas ignite will deal additive damage. If you know you will be laning against a ridiculous self-heal champion (especially Volibear, Xin or Aatrox), then feel free to take Ignite.

During early-mid game there are certain situations in which you might hold off self-healing with Bloodlust to continue benefiting from the bonus 35% Crit chance that max Fury gives. However, with 94% Crit chance, you don't need that extra Fury. Burn it. Try using Bloodlust as early as possible in a teamfight. If you get focused and are forced to use Undying Rage, your Fury will instantly maximize. At 40% Cooldown Reduction, Bloodlust's cooldown is 7.2 seconds, and Undying Rage lasts for 5 seconds. In other words, as long as you held out for at least 2.2 seconds in a teamfight after your first use of Bloodlust, you will be able to heal a second time by the time your ultimate expires.

Thanks goes out to CT Fletcher for reinforcing my confidence in this build.
"And not a curl was done..."

a.k.a. Try it.

Siv!
I would be honored if you brought life to this guide on youtube, preferably in HD.