This build is still under construction.

Spinning Slash first gets you out of bad situations early game. You are squishy until level six and its important to get your escape mechanism first.

Bloodlust - easily your best ability (besides your ult), get it leveled up quickly.

Mocking Shout - You want to level this one up second. Also, make sure you use this during team fights at the beginning of the fight. It reduces the damage output of enemies nearby and a lot of Tryndamere players forget to use this ability properly.

Spinning Slash - This is a gap closer, so there is no need to level it past level 1 until you absolutely have to.

It's important to remember that Tryndamere's rage system is built off an ATTACK SPEED system. Therefore, Black Cleaver and Zeal not only give you movement speed and armor pen, but they give you the attack speed needed during the early game.

You are squishy. REALLY squishy. Don't die, play smart, and don't die. Turret hug if you must and make sure to only use spinning slash to get OUT of situations, not to get in. Use your slow to catch up and exhaust to stay within range, if they get out of melee range, go back to killing minions. Its essential not to blow your spinning slash running after someone during this phase of the game because any player that knows Tryndamere at all will just turn around and kill you cuz you can't get away.

You can start to take risks now. As soon as you hit level 6, I always just burst down the lane and see if anyone is stupid enough to not run back to their turret. If they stay, kill them, if they run, try to kill them before they get to the turret, if they get to the turret and they only have like 1 hit left, dive them hard and get out.

Make sure to take note of where the enemy jungler is before you do this.

As soon as you build Bloodthirster, you've got to calm down. You can't be kill trading and turret diving unless you know you can win and get out clean. Basically, you're back in the same boat you were earlier, try not to die, kill things, and try not to die.

Be careful not to get too far away from your team. Yes, you will end up solo farming the lanes because Tryndamere is amazing at farming late game, but you need to be very aware of what your team is doing, and if they've already engaged the other team, its too late, you were too far out of position, just push the lane you're in.

Question #1 - Why not stack Phantom Dancers?
There is some truth to the fact that you can't chase well with this build, but here's why it doesn't matter: YOU'RE TWO SHOTTING THEM. You don't need to chase, you need to kill them quick and move onto the next one. Also, Tryndamere can't chase very well anyway, and if you think he can, you're lying to yourself. He can lead people on a chase all day as the person being chased, but honestly, his slow doesn't last long enough to chase a ranged anyway and you'll just be kited until their teammates come to help. If you can't kill a ranged in 2 or 3 hits, there's no reason for you to stick around, just get out, let them b, and take the other team on 5v4.

Question #2 - Why not build Frozen Mallet?
Bottom line: its a dumb move. You're buying an item that has health on it... If you don't see the problem with that, you shouldn't have bought Tryndamere. Also, if you're not good enough to use mocking shout to slow the people you need, Frozen Mallet isn't going to fix that, practice and a higher IQ will fix that. Basically, you don't need health and you already have a slow, so you're getting a total of 20 Attack Damage out of one item.