WPF was really designed with the possibility to change the look and behavior of every out-of-the-box mechanisms / controls (buttons, menus, treeview, etc.). So, in general, it's better to do this rather than to rewrite everything. For example, if you redesign your custom menu, you'll have to think about keyboard, UI automation, etc...

So, I gave a shot at your example and tried to build a minimum working sample - pure XAML - that mimics VS online menu (I've also added the hover background color change that's not by default in WPF's menu).

Here is the result and, as you see, it looks very similar:

Here is the XAML. I've chosen to use a custom control template per each MenuItem. I think it's quite practical when you need to really customize every item.

<Window x:Class="WpfApp1.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        Title="MainWindow" Height="550" Width="525">
    <Window.Resources>
        <BooleanToVisibilityConverter x:Key="btv" />

        <!-- style a top level menu item -->
        <ControlTemplate x:Key="VsMenuTop" TargetType="MenuItem">
            <StackPanel TextBlock.FontSize="15px" Height="40">
                <!-- label, icons, etc. -->
                <Label Content="{TemplateBinding Header}" Margin="5" Foreground="White" />

                <!-- sub items -->
                <Popup IsOpen="{TemplateBinding IsSubmenuOpen}" AllowsTransparency="True" Focusable="False">
                    <Border BorderThickness="1" Background="White" BorderBrush="#E0E0E0">
                        <StackPanel IsItemsHost="True" />
                    </Border>
                </Popup>
                <StackPanel.Style>
                    <Style TargetType="StackPanel">
                        <Style.Triggers>
                            <Trigger Property="IsMouseOver"  Value="True">
                                <Setter Property="Background" Value="#106EBE" />
                            </Trigger>
                        </Style.Triggers>
                    </Style>
                </StackPanel.Style>
            </StackPanel>
        </ControlTemplate>

        <!-- style a non-top level menu item -->
        <ControlTemplate x:Key="VsMenuSub" TargetType="MenuItem">
            <DockPanel TextBlock.FontSize="15px" x:Name="panel">
                <!-- label, icons, etc. -->
                <Image Source="{Binding Icon, RelativeSource={RelativeSource TemplatedParent}}" Width="20" Margin="5,0" />
                <Label Content="{TemplateBinding Header}" Foreground="Black" Margin="0,5,5,5" />

                <!-- draw the right arrow only if this menu item has sub items -->
                <Image Source="icon_right.png" Visibility="{Binding HasItems, Converter={StaticResource btv}, RelativeSource={RelativeSource TemplatedParent}}" />

                <!-- sub items -->
                <Popup IsOpen="{TemplateBinding IsSubmenuOpen}" AllowsTransparency="True" Focusable="False" Placement="Right" >
                    <Border BorderThickness="1" Background="White" BorderBrush="#E0E0E0">
                        <StackPanel IsItemsHost="True" />
                    </Border>
                </Popup>
            </DockPanel>
            <ControlTemplate.Triggers>
                <Trigger Property="IsHighlighted" Value="True">
                    <Setter Property="Background" TargetName="panel" Value="#EFF6FC" />
                </Trigger>
            </ControlTemplate.Triggers>
        </ControlTemplate>

        <!-- style the separator -->
        <ControlTemplate x:Key="VsMenuSep" TargetType="Separator">
            <Border Height="1" Background="#E0E0E0" />
        </ControlTemplate>

        <!-- style the VSOnline -->
        <ControlTemplate x:Key="VsOnline" TargetType="MenuItem">
            <StackPanel TextBlock.FontSize="15px" Height="40" Orientation="Horizontal" Background="#005A9E">
                <Label Content="{TemplateBinding Header}" Margin="5" Foreground="White" />
                <Image Source="icon_down.png" Height="20" Margin="0,0,5,0" />

                <!-- sub items -->
                <Popup IsOpen="{TemplateBinding IsSubmenuOpen}" AllowsTransparency="True" Focusable="False">
                    <Border BorderThickness="1" Background="White" BorderBrush="#E0E0E0">
                        <StackPanel IsItemsHost="True" />
                    </Border>
                </Popup>
            </StackPanel>
        </ControlTemplate>

        <!-- some base stuff -->
        <Style TargetType="Menu">
            <Setter Property="Background" Value="#0078D7" />
            <Setter Property="Height" Value="40px" />
        </Style>

    </Window.Resources>

    <!-- the real app and real menu -->
    <StackPanel>
        <Menu IsMainMenu="True">
            <MenuItem Header="_VSOnline" Template="{StaticResource VsOnline}" >
                <MenuItem Header="_Whatever" Template="{StaticResource VsMenuSub}" />
            </MenuItem>
            <MenuItem Header="_Dashboards" Template="{StaticResource VsMenuTop}">
                <MenuItem Header="_Overview" Template="{StaticResource VsMenuSub}" />
            </MenuItem>
            <MenuItem Header="_Code" Template="{StaticResource VsMenuTop}">
                <MenuItem Header="_Files" Template="{StaticResource VsMenuSub}" />
                <MenuItem Header="_Commits" Template="{StaticResource VsMenuSub}" />
                <MenuItem Header="_Pushes" Template="{StaticResource VsMenuSub}" />
            </MenuItem>
            <MenuItem Header="_Work" Template="{StaticResource VsMenuTop}">
                <MenuItem Header="_Backlogs" Template="{StaticResource VsMenuSub}" Icon="icon_backlogs.png" />
                <MenuItem Header="_Queries" Template="{StaticResource VsMenuSub}" Icon="icon_queries.png" />
                <Separator Template="{StaticResource VsMenuSep}" />
                <MenuItem Header="_New Work Item" Template="{StaticResource VsMenuSub}">
                    <MenuItem Header="_Epic" Template="{StaticResource VsMenuSub}" Icon="icon_epic.png" />
                    <MenuItem Header="_Feature" Template="{StaticResource VsMenuSub}" Icon="icon_feature.png" />
                    <MenuItem Header="_Issue" Template="{StaticResource VsMenuSub}" Icon="icon_issue.png" />
                    <MenuItem Header="_Task" Template="{StaticResource VsMenuSub}" Icon="icon_task.png" />
                    <MenuItem Header="_Test Case" Template="{StaticResource VsMenuSub}" Icon="icon_testcase.png" />
                    <MenuItem Header="_User Story" Template="{StaticResource VsMenuSub}" Icon="icon_userstory.png" />
                </MenuItem>
                <MenuItem Header="_Bug" Template="{StaticResource VsMenuSub}" Icon="icon_bug.png" />
            </MenuItem>
        </Menu>
    </StackPanel>
</Window>

The project is available here on github.