You are searching for a subset of

.../MAPPING/TRANSFORMATION/@TYPE/TRANSFORMFIELD/@TYPE
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An attribute cannot have a child element, so that can't possibly match. Solution:

for ($root->findnodes(
    '/POWERMART/REPOSITORY/FOLDER/MAPPING' .
    '/TRANSFORMATION[@TYPE="Sequence"]' .
    '/TRANSFORMFIELD[@TYPE="bigint"]'
)) {
    $_->setAttribute('TYPE', 'integer');
}
[download]

Square brackets specify which nodes to filter through, like a SELECT clause in SQL.