void Start()
{
    // Set text
    TMP_Text textMesh = GetComponent<TMP_Text>();
    textMesh.text = "DETERMINATION";

    CharTweener tweener = textMesh.GetCharTweener();
    for (int i = 0; i < tweener.CharacterCount; i++)
    {
        // Move characters in a circle
        Tween circleTween = tweener.DOMoveCircle(i, 0.05f, 0.5f)
            .SetLoops(-1, LoopType.Restart);

        // Fade character color between yellow and white
        Tween colorTween = tweener.DOColor(i, Color.yellow, 0.5f)
            .SetLoops(-1, LoopType.Yoyo);

        // Offset animations based on character index in string
        float timeOffset = (float)i / tweener.CharacterCount;
        circleTween.fullPosition = timeOffset;
        colorTween.fullPosition = timeOffset;
    }
}

Use DOTween tweens on TextMeshPro characters the same way you would on a game object:

transform.DOMove(Vector3.zero, 1) // Move the transform to (0,0,0) over 1 second
// becomes...
tweener.DOMove(2, Vector3.zero, 1); // Move the 3rd character in the text mesh to (0,0,0) over 1 second

You can also set properties on characters:

transform.localPosition = new Vector3(0,1,0) // Move the transform to (0,1,0) locally
// becomes...
tweener.SetOffsetPosition(2, new Vector3(0,1,0)); // Move the 3rd character in the text mesh to (0,1,0) above its original position

CharTween extends existing features for use on text:

• Use Transform tweens on characters (DOMove, DORotate, DOLookAt)
• Use Transform properties and methods on characters (Get/SetPosition, Get/SetRotation, LookAt)
• Use Color and VertexGradient tweens on characters (DOColor, DOFade, DOGradient)
• Use Color and VertexGradient properties on characters (Get/SetColor, Get/SetAlpha, Get/SetColorGradient)
• Use Tween properties and methods on character tweens (Pause, OnComplete, timeScale)

CharTween also provides some extras:

• Use extra tweens that aren't in DOTween (DOMoveCircle, DODriftPosition/Rotation)
• Edit character position as offset from start position (DOOffsetMove, GetStartPosition, Get/SetOffsetPosition)
• Tween "ahead of time". For example, run tweens on a TMP_InputField for characters that haven't been typed yet, and they will show up animated
  • Does not work with DOMove or DOLocalMove. To tween position ahead of time, use DOOffsetMove. DoShakePosition and DOPunchPosition also work

• Cannot tween a text mesh before its Awake() has been called, must wait until Start() or later
• Material effects such as Outline, Glow, and Underlay cannot be changed per-character
• Text mesh effects such as Underline, Strikethrough cannot be changed per-character
• Performance overhead, creates one Transform per modified character.

• Unity 2018.1.0f2 or newer
• TextMesh Pro 1.3.0 (in Unity 2018.1.0f2 package manager) or newer
• DOTween 1.1.695 (February 02, 2018) or newer
  • DOTween 1.2.320 (January 07, 2020) and older require small changes, see below

1. Have DOTween and TextMeshPro in your project
2. Get the .unitypackage from the latest release
3. Open and import, exclude the Examples folder if needed
4. See fix for old DOTween version if needed

Applies to DOTween 1.2.320 (January 07, 2020) and older

/*** VertexGradientPlugin.cs, lines 30-34 ***/

        // COMMENT this method if DOTween version is 1.2.320 or older
        public override void SetFrom(TweenerCore<VertexGradient, VertexGradient, NoOptions> t, VertexGradient fromValue, bool setImmediately, bool isRelative) { SetFrom(t, isRelative); }

        // UNCOMMENT this method if DOTween version is 1.2.320 to 1.2.235
        //public override void SetFrom(TweenerCore<VertexGradient, VertexGradient, NoOptions> t, VertexGradient fromValue, bool setImmediately) { SetFrom(t, false); }

MIT