As mentioned, it's easier to just rebuild the XML.

A slightly shorter syntax than the other answer, and the benefit is that you don't need to rebuild everything.

Just select out everything else apart from <Key> using .query and add it as an unnamed column

DECLARE @XMLDocument XML = '
<Root>
    <MainNode>
        <Key>10</Key>
        <Info></Info>
    </MainNode>
    <MainNode>
        <Key>13</Key>
        <Info>15</Info>
        <Info>18</Info>
    </MainNode>
</Root>';

SELECT
  R.MN.value('(Key/text())[1]','int') AS [@Key],
  R.MN.query('*[local-name() != "key"]')
FROM @XMLDocument.nodes('/Root/MainNode')R(MN)
FOR XML PATH('MainNode'), ROOT('Root'), TYPE;

db<>fiddle

It is better to use SQL Server native XQuery functionality via FLWOR expression.

It allows to compose a desired output XML "visually".

Check it out below.

SQL

DECLARE @XMLDocument XML = 
N'<Root>
    <MainNode>
        <Key>10</Key>
        <Info></Info>
    </MainNode>
    <MainNode>
        <Key>13</Key>
        <Info>15</Info>
        <Info>18</Info>
    </MainNode>
</Root>';

SELECT @XMLDocument.query('<Root>
    {
        for $x in /Root/MainNode
        return <MainNode Key="{$x/Key}">
            {$x/*[not(local-name()="Key")]}
            </MainNode>
    }
</Root>');

Output

<Root>
  <MainNode Key="10">
    <Info />
  </MainNode>
  <MainNode Key="13">
    <Info>15</Info>
    <Info>18</Info>
  </MainNode>
</Root>

As siggemannen commented, this might be easier by consuming the XML and creating new XML from that. You can then easily move the key from a node to an attribute by aliasing it as [@Key] :

DECLARE @XMLDocument XML = '
<Root>
    <MainNode>
        <Key>10</Key>
        <Info></Info>
    </MainNode>
    <MainNode>
        <Key>13</Key>
        <Info>15</Info>
        <Info>18</Info>
    </MainNode>
</Root>';

SELECT R.MN.value('(Key/text())[1]','int') AS [@Key],
       (SELECT ISNULL(MN.I.value('(./text())[1]','varchar(10)'),'') AS Info --As you want a blank row we need to use a string, as '' would be 0 as a int.
        FROM  R.MN.nodes('Info') MN(I)
        FOR XML PATH(''),TYPE)
FROM @XMLDocument.nodes('/Root/MainNode')R(MN)
FOR XML PATH('MainNode'),ROOT('Root');