UnityEngine.UI.Textにアタッチして文字を個別に動かすアニメーションのサンプル。

CommonTextAnimation.cs

//-------------------------------------------------------
// @file   CommonTextAnimation.cs
// @brief  IMeshModifierを利用したテキストアニメーション.
//
// @author haruki.tachihara
//-------------------------------------------------------
using System.Collections;
using System.Collections.Generic;
using UnityEngine;
using UnityEngine.EventSystems;

//これは別UnityEngine名前空間を使ってはいるが自前のTweenライブラリ
using Method = UnityEngine.UI.TweenMain.Method;

namespace UnityEngine.UI
{
[RequireComponent(typeof(Text))]
[DisallowMultipleComponent]
public class CommonTextAnimation : BaseMeshEffect
{
    // 1文字は6頂点.
    const int CHAR_VERT_CNT = 6;

    #region Animation Parameter

    // OnEnableで自動開始するか.
    public bool autoStartOnEnable = true;
    // アニメーションにかける所用時間 [秒]
    public float duration = 0.5f;
    // X軸の動きの大きさ.
    public float moveAmountX = 0f;
    // Y軸の動きの大きさ.
    public float moveAmountY = 0f;
    // シェイクは有効か.
    public bool enableShake = true;
    // シェイク量.
    public float shakeAmount = 1f;

    #endregion

    private bool isFinished;
    private float time;

    public void StartEffect()
    {
        time = 0;
        isFinished = false;
    }

    protected override void OnEnable()
    {
        base.OnEnable();
        if (autoStartOnEnable)
        {
            StartEffect();
        }
    }

    protected virtual void Update()
    {
        if (isFinished)
            return;

        time += Time.deltaTime;
        if (graphic != null)
        {
            graphic.SetVerticesDirty();
        }
    }

    public override void ModifyMesh(VertexHelper vh)
    {
        var vList = new List<UIVertex>();
        vh.GetUIVertexStream(vList);

        Modify(ref vList);

        vh.Clear();
        vh.AddUIVertexTriangleStream(vList);
    }

    void Modify(ref List<UIVertex> vList)
    {

        if (isFinished || duration <= 0f || vList.Count < CHAR_VERT_CNT)
        {
            return;
        }
        if (time >= duration && !enableShake)
        {
            isFinished = true;
        }

        var vertexCount = vList.Count;
        var charCount = vertexCount / CHAR_VERT_CNT;
        var deltaTimeParChar = duration / charCount;
        Vector3 shake = Vector3.zero;

        if (enableShake)
        {
            shake = Random.insideUnitCircle * shakeAmount;
        }

        for (int i = 0; i < vertexCount; i += CHAR_VERT_CNT)
        {
            // 現在の文字のnormalizeTime[0-1]を計算.
            var startTime = i / CHAR_VERT_CNT * deltaTimeParChar;
            var elapsedTime = time - startTime;
            var normalizeTime = Mathf.Clamp01(elapsedTime / deltaTimeParChar);

            if (normalizeTime <= 0f)
            {
                // 見えないように設定.
                for (int vertexIndex = 0; vertexIndex < CHAR_VERT_CNT; vertexIndex++)
                {
                    var v = vList[i + vertexIndex];
                    v.color = Color.clear;
                    vList[i + vertexIndex] = v;
                }
            }
            else if (normalizeTime >= 1f)
            {
                if (enableShake)
                {
                    for (int vertexIndex = 0; vertexIndex < CHAR_VERT_CNT; vertexIndex++)
                    {
                        var v = vList[i + vertexIndex];
                        v.position += shake;
                        vList[i + vertexIndex] = v;
                    }
                }
            }
            else
            {
                // アニメーションさせる.
                var center = Vector2.Lerp(vList[i].position, vList[i + 3].position, 0.5f);

                for (int vertexIndex = 0; vertexIndex < CHAR_VERT_CNT; vertexIndex++)
                {
                    var v = vList[i + vertexIndex];
                    var sampled = Tweening.Sample(Method.EaseOut, normalizeTime);

                    // 移動量
                    var moveX = moveAmountX * Tweening.Sample(Method.EaseIn, 1f - normalizeTime);
                    var moveY = moveAmountY * Mathf.Sin((1f - normalizeTime) * Mathf.PI);//上下にサインカーブ移動.

                    // スケール
                    var posX = Mathf.Lerp(center.x, v.position.x, sampled) + moveX;
                    var posY = Mathf.Lerp(center.y, v.position.y, sampled) + moveY;

                    v.position = new Vector2(posX + shake.x, posY + shake.y);

                    vList[i + vertexIndex] = v;
                }
            }
        }
    }
}

public static class Tweening
{
    public static float Sample(Method method, float normalizeTime)
    {
        float val = Mathf.Clamp01(normalizeTime);

        switch (method)
        {
            case Method.Linear:
                val = Easing.Linear(val);
                break;

            case Method.EaseIn:
                val = Easing.Sinusoidal.In(val);
                break;

            case Method.EaseOut:
                val = Easing.Sinusoidal.Out(val);
                break;

            case Method.EaseInOut:
                val = Easing.Sinusoidal.InOut(val);
                break;

            case Method.BounceIn:
                val = Easing.Bounce.In(val);
                break;

            case Method.BounceOut:
                val = Easing.Bounce.Out(val);
                break;

            case Method.BounceInOut:
                val = Easing.Bounce.InOut(val);
                break;
        }
        return val;
    }
}
}