unbedingt
definitely
Expresses that something should or must happen in any case or under all circumstances; absolutely, necessarily.
Diesen Film musst du dir unbedingt ansehen!
You definitely have to watch this film!

definitely / unconditional
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definitely
Expresses that something should or must happen in any case or under all circumstances; absolutely, necessarily.
Diesen Film musst du dir unbedingt ansehen!
You definitely have to watch this film!

The word is made up of 'un-' (a negation) and 'bedingt' (conditional). 'Bedingt' comes from 'die Bedingung' (condition). So 'unbedingt' literally means 'without condition', which explains the two main meanings.
Er schenkte ihr sein unbedingtes Vertrauen.
He gave her his unconditional trust.
As an adverb meaning 'auf jeden Fall' (in any case / definitely), 'unbedingt' usually appears in the middle of the sentence. It is very often combined with modal verbs like 'müssen' (must) or 'sollen' (should) to express an urgent recommendation or necessity.
Du musst dir diesen Film unbedingt ansehen!
You definitely have to watch this film!
When 'unbedingt' appears before a noun and is declined like an adjective, it means 'unrestricted' or 'absolute'. Typical combinations are 'unbedingter Gehorsam' (unconditional obedience), 'unbedingtes Vertrauen' (unconditional trust), or 'ein unbedingter Wille' (an absolute will).
Für diesen Job braucht man den unbedingten Willen zum Erfolg.
For this job, you need the absolute will to succeed.
case / fall
'auf jeden Fall' and 'unbedingt' can both express that something should definitely happen or is very important. 'auf jeden Fall' is a fixed expression with 'Fall' and often means 'definitely' or 'under all circumstances'. 'unbedingt' is an adverb and is placed directly with a verb or statement. In many everyday sentences, the two are similar, but they do not always sound equally natural. 'Komm auf jeden Fall!' and 'Komm unbedingt!' mean almost the same thing. 'unbedingt' often places stronger emphasis on a wish or a necessity.

Heute muss sie unbedingt die Unterlagen für das Amt abgeben.
Today she absolutely has to submit the documents for the public office.
Du musst mir auf jeden Fall schreiben, wenn du angekommen bist.
You definitely have to write to me when you've arrived.