After I had read the Monster Manual's Tarrasque entry, I began thinking of ways to kill it. The first thing that came to mind is for 1 party member to become a creature that is Huge in size, then grapple the Tarrasque while other members of the party attacked it.

My idea is to have a Level 20 Variant Human with at least 13 STR and 20 INT with the War Caster and Grappler feats. Before the battle, they would use the 9th level spell Shapechange to turn into a Storm Giant. As the battle begins, he would attempt to grapple the Tarrasque. It wouldn't be guaranteed, but it would still be possible because the storm giant overall has a +4 over the Tarrasque's Athletics, and has advantage. This makes the probability of the character winning to (check my math) around 80%.

Once the Tarrasque is grappled, the Storm Giant would use subsequent turns to re-grapple if it escapes, or to use their action to make it restrained. While this is happening, other party members would be supporting the giant or nuking the Tarrasque with magical bows. And every time the giant was hit, he would get advantage and +10 to the concentration saving throw.

My optimal party composition would be 1 or 2 Life Clerics or similar healers who are constantly healing the Storm Giant, 3 fighters with magical bows, and 1 Wizard or Sorcerer who are buffing the Storm Giant and the rest of the fighting force.

When you use the Shapechange spell, do you keep all of the character's feats? And is the Tarrasque being grappled affected by his Legendary Resistance?

Yes, you can grapple the tarrasque

As discussed in this question, you keep the benefit of your feats when you shapechange. And you're correct that Legendary Resistance won't let the tarrasque avoid a grapple.

But that won't stop it from attacking you

Even if you pin the tarrasque with your grappler feat, all that does is give it disadvantage on its attacks against you. Its attacks are at +19 to hit, and a storm giant's AC is 16, so the disadvantage won't help you very much.

The tarrasque does an average of 212 damage per round (its attacks average 36, 28, 28, 32, 24 damage; it also gets legendary actions which can be two more attacks for 28 and 36 damage).

And that's okay

It appears that the tarrasque's attacks are nonmagical (!), so a stoneskin spell will halve the incoming damage. Your concentration checks seem surprisingly safe: the storm giant gets +10 to his constitution save, and with the stoneskin spell you're unlikely to need more than a DC10 save.

Two high-level clerics can heal you through the damage for several rounds (heal restores 10hp per level of the spell slot).

But the main thing you're getting from this grappling thing is you're forcing the tarrasque to attack you (with your stoneskin spell, and with your size making you too large to swallow) rather than attack one of your more fragile allies. And you're giving your allies advantage on their attack rolls, once the tarrasque is restrained.

That seems worthwhile.