Help the heavily scratched pet owner complete their text message about a failed wardrobe change.

_____, I simply could not get the festive holiday sweater onto Mr. Fluffles.

The correct answer is Try as I might.

Try as I might (or Try as he might, etc.) is a fixed, advanced concessive structure meaning "No matter how hard I tried." It always uses the bare infinitive try, never the participle trying.

Despite must be followed by a noun, pronoun, or gerund, not a full clause. However hard did I try is incorrect because we do not use question word order (inversion) after however in a concessive clause.