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She heaped on lavish, indiscriminate praise.
Literal
[topic-は] indiscriminately praised-to-pieces.
やたらと ('excessively, indiscriminately, without restraint') is an adverb expressing unmoderated, excessive behavior — often with a slightly negative or bemused tone. 誉めちぎる ('to praise to pieces, lavish praise') is a compound: 誉める ('to praise') + ちぎる ('to tear off'); the auxiliary ちぎる as a verb suffix functions as an intensifier meaning 'thoroughly, to extremes.' Compare 食べちぎる (rare; eat to pieces), 言いちぎる (criticize sharply). The combination paints a picture of over-the-top, almost embarrassing flattery.