vollends
completely
Expresses that something happens completely, entirely, or finally.
Nach dem letzten Fehler war er vollends verwirrt.
After the last mistake, he was completely confused.

completely
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completely
Expresses that something happens completely, entirely, or finally.
Nach dem letzten Fehler war er vollends verwirrt.
After the last mistake, he was completely confused.

'Vollends' can be derived from 'voll' (full) and 'Ende' (end). It describes a state that has reached its 'full end' and is therefore complete or final.
Nach dieser Nachricht verlor er vollends die Fassung.
After this news, he completely lost his composure.
As an adverb, 'vollends' usually stands directly before the word (often an adjective or participle) that it is meant to intensify. This position gives the expression special emphasis.
Das alte Haus war nach dem Sturm vollends zerstört.
The old house was completely destroyed after the storm.
'Vollends' is a word of elevated style and is used mainly in written language. It sounds more formal and expresses a stronger sense of finality.
Mit dieser Entscheidung waren seine Pläne vollends gescheitert.
With this decision, his plans had completely failed.
completely
'völlig' and 'vollends' both express that something is entirely or completely the case. 'völlig' is very normal in everyday language and can strongly intensify many adjectives or statements, for example 'völlig müde' (completely tired) or 'völlig falsch' (completely wrong). 'vollends' sounds somewhat more elevated and fits especially when a state is reached finally or completely. In many sentences, 'völlig' is more natural, while 'vollends' sounds more like a final step or completion.

Nach der zweiten schlechten Nachricht war Nele vollends verunsichert.
After the second piece of bad news, Nele was completely unsettled.
Nach dem langen Einkauf war ich völlig erschöpft.
After the long shopping trip, I was completely exhausted.