Just apply this style to your textbox. This is the only way you can do it.
<Style x:Key="TextBoxStyle1" TargetType="TextBox">
<Setter Property="BorderThickness" Value="1"/>
<Setter Property="Background" Value="#FFFFFFFF"/>
<Setter Property="Foreground" Value="#FF000000"/>
<Setter Property="Padding" Value="2"/>
<Setter Property="BorderBrush">
<Setter.Value>
<LinearGradientBrush EndPoint="0.5,1" StartPoint="0.5,0">
<GradientStop Color="#FFA3AEB9" Offset="0"/>
<GradientStop Color="#FF8399A9" Offset="0.375"/>
<GradientStop Color="#FF718597" Offset="0.375"/>
<GradientStop Color="#FF617584" Offset="1"/>
</LinearGradientBrush>
</Setter.Value>
</Setter>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="TextBox">
<Grid x:Name="RootElement">
<VisualStateManager.VisualStateGroups>
<VisualStateGroup x:Name="CommonStates">
<VisualState x:Name="Normal"/>
<VisualState x:Name="MouseOver">
</VisualState>
<VisualState x:Name="Disabled">
<Storyboard>
<DoubleAnimation Duration="0" To="1" Storyboard.TargetProperty="Opacity" Storyboard.TargetName="DisabledVisualElement"/>
</Storyboard>
</VisualState>
<VisualState x:Name="ReadOnly">
<Storyboard>
<DoubleAnimation Duration="0" To="1" Storyboard.TargetProperty="Opacity" Storyboard.TargetName="ReadOnlyVisualElement"/>
</Storyboard>
</VisualState>
</VisualStateGroup>
<VisualStateGroup x:Name="FocusStates">
<VisualState x:Name="Focused">
</VisualState>
<VisualState x:Name="Unfocused">
</VisualState>
</VisualStateGroup>
<VisualStateGroup x:Name="ValidationStates">
<VisualState x:Name="Valid"/>
<VisualState x:Name="InvalidUnfocused">
<Storyboard>
<ObjectAnimationUsingKeyFrames Storyboard.TargetProperty="Visibility" Storyboard.TargetName="ValidationErrorElement">
<DiscreteObjectKeyFrame KeyTime="0">
<DiscreteObjectKeyFrame.Value>
<Visibility>Visible</Visibility>
</DiscreteObjectKeyFrame.Value>
</DiscreteObjectKeyFrame>
</ObjectAnimationUsingKeyFrames>
</Storyboard>
</VisualState>
<VisualState x:Name="InvalidFocused">
<Storyboard>
<ObjectAnimationUsingKeyFrames Storyboard.TargetProperty="Visibility" Storyboard.TargetName="ValidationErrorElement">
<DiscreteObjectKeyFrame KeyTime="0">
<DiscreteObjectKeyFrame.Value>
<Visibility>Visible</Visibility>
</DiscreteObjectKeyFrame.Value>
</DiscreteObjectKeyFrame>
</ObjectAnimationUsingKeyFrames>
<ObjectAnimationUsingKeyFrames Storyboard.TargetProperty="IsOpen" Storyboard.TargetName="validationTooltip">
<DiscreteObjectKeyFrame KeyTime="0">
<DiscreteObjectKeyFrame.Value>
<System:Boolean>True</System:Boolean>
</DiscreteObjectKeyFrame.Value>
</DiscreteObjectKeyFrame>
</ObjectAnimationUsingKeyFrames>
</Storyboard>
</VisualState>
</VisualStateGroup>
</VisualStateManager.VisualStateGroups>
<Grid>
<Border x:Name="ReadOnlyVisualElement" Background="#5EC9C9C9" Opacity="0"/>
<Border x:Name="MouseOverBorder" BorderBrush="Transparent" BorderThickness="1">
<ScrollViewer x:Name="ContentElement" BorderThickness="0" IsTabStop="False" Padding="{TemplateBinding Padding}"/>
</Border>
</Grid>
<Border x:Name="DisabledVisualElement" BorderBrush="#A5F7F7F7" BorderThickness="{TemplateBinding BorderThickness}" Background="#A5F7F7F7" IsHitTestVisible="False" Opacity="0"/>
<Border x:Name="ValidationErrorElement" BorderBrush="#FFDB000C" BorderThickness="1" CornerRadius="1" Visibility="Collapsed">
<ToolTipService.ToolTip>
<ToolTip x:Name="validationTooltip" DataContext="{Binding RelativeSource={RelativeSource TemplatedParent}}" Placement="Right" PlacementTarget="{Binding RelativeSource={RelativeSource TemplatedParent}}" >
<ToolTip.Triggers>
<EventTrigger RoutedEvent="Canvas.Loaded">
<BeginStoryboard>
<Storyboard>
<ObjectAnimationUsingKeyFrames Storyboard.TargetProperty="IsHitTestVisible" Storyboard.TargetName="validationTooltip">
<DiscreteObjectKeyFrame KeyTime="0">
<DiscreteObjectKeyFrame.Value>
<System:Boolean>true</System:Boolean>
</DiscreteObjectKeyFrame.Value>
</DiscreteObjectKeyFrame>
</ObjectAnimationUsingKeyFrames>
</Storyboard>
</BeginStoryboard>
</EventTrigger>
</ToolTip.Triggers>
</ToolTip>
</ToolTipService.ToolTip>
<Grid Background="Transparent" HorizontalAlignment="Right" Height="12" Margin="1,-4,-4,0" VerticalAlignment="Top" Width="12">
<Path Data="M 1,0 L6,0 A 2,2 90 0 1 8,2 L8,7 z" Fill="#FFDC000C" Margin="1,3,0,0"/>
<Path Data="M 0,0 L2,0 L 8,6 L8,8" Fill="#ffffff" Margin="1,3,0,0"/>
</Grid>
</Border>
</Grid>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>