The Moves
Before you can defeat "Tigger", the first thing you must do is learn his moves and to anticipate them. On that note, here is a list of the ones that I have noticed.

The Charge
Tigrex runs at you. He doesn't track you very sharply, but he moves fast, and if you don't get out of the way quick, chances are you are going to be missing a large chunk of your health. Also, just because you avoided his charge once doesn't necessarily mean that you're safe. Sometimes he will skid and turn at the end of the charge, and come running at you once again. When in rage mode, he can turn once more, to come charging at you for a grand total of 3 times. Also, his charges are somewhat homing if you are too far away, so consider yourself warned.

The Spin
Sometimes when you are too close to him, he will spin in a circle, knocking you back. Not too hard to avoid or damaging when you know what to look for. It can be easily blocked as well by simply facing him and guarding. Don't try to guard in the direction he is spinning. You can tell he is going to do this when he lowers his body slightly and curls his tail to his right. DO NOT stay at its right side, because while spinning, it extends its left arm.

The Leap
Tigrex will jump through the air at you. Easy to avoid, but fairly damaging if it hits you. Note*: When in rage mode, "Tigger" will never jump just once. He will always jump twice, and the second jump will be followed by his "Hit-me-now Stance." For this to happen he has to be in rage mode.

The Bite
Tigrex has two different bite attacks, the long one and the short one. Both of which can be painful and annoying if you get caught in the middle of a combo. Right before he does this, he raises his head slightly to the right and leans back a little.

The Roar
Nine times out of ten, when Tigrex leaps back and uses this move, he will go into rage mode. You can tell he's about to do this when he plants his limbs, and sits straight up. It doesn't have a very big range, but it has two different affects depending on how close to him you are. If you are standing right next to him, you will be sent flying. If you are sort of close, then you will be stunned instead. A little ways away, and you won't be affected at all. If he does roar, you have two options.
1) If you are far enough away from him, simply run furthur away. This way you won't get stunned or blasted away.
2) If you are right up next to him attacking, your best bet is to stay there and take the blast. It will send you flying and take away damage, but not nearly as much as you would had you been stunned and he ran you over.
Oh, and you can block it too I suppose.
* Also, with a well - perfect timed roll or leap, yu can avoid being hit or affected by it's roar in any way. But ONLY try this when yu are more experienced with him.
Remember, negligence will be punished :)

The Push
Tigrex will lean backwards some and push a bunch of giant snowballs or rocks at you which will spread out the further they go. If you are paying attention, it's not too hard to dodge, but it does hurt a lot if it hits. The tail also whips round to the right, catching even experienced hunters unawares.

RAGE MODE
This got its own box and capital letters because this is probably the most important thing to know, especially for new players. When Tigrex goes into rage mode, he jumps back and roars. Red veins stand out on his forearms and he gets much faster and stronger. Do NOT attack him when he is in rage mode. I cannot stress this enough. Put your weapon away and run around like a little girl, but do not attack him. The only time it is safe to attack Tigrex when he is in rage mode is when he jumps twice. Every time he jumps twice, he will follow it with his Hit-Me-Now Stance. If you want, feel free to oblige him. Just don't get greedy with your combos...
NOTE:The Tigrex loses 45% of his defense while in rage mode, so attacking him while he is in rage mode with a powerful weapon is very effective especially with G.swords,Long swords and Hammers.This also works best while Tigrex is in the "Hit me Now"stance.

Strategies
Now you know, at least by description, what his moves are. Now, its time to figure out how to put that knowledge to use. Also, this goes for all of the different weapon types. Make sure you are safe before you use an item. It does you no good if as soon as you use it, you get run over by Tigrex. Then, you just need it to use another one. And it is almost always better to heal if you have the chance than it is to do damage. Parts of the strategies for the different weapons are similar, nearly identical actually, so you do not need to read all the strategies for the different weapons. Actually, I designed this with the expectation that you would skip straight the sections you wanted, so if you notice some repetition in places, that's the reason.