dogged / grim
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dogged
Fixed on a goal in a very persistent and often tense way, without ease or flexibility. It describes an intense, almost grim determination.
Sie trainierte verbissen für den Marathon, um ihre persönliche Bestzeit zu unterbieten.
She trained doggedly for the marathon in order to beat her personal best.
'Verbissen' is the past participle of the verb 'sich verbeißen' (to bite into something and not let go; to become fixated on something). Figuratively, it describes how a dog bites into something and no longer lets go. This persistence is transferred to people and their actions or facial expressions.
Er hat sich in die Idee verbissen und hört auf keine Ratschläge mehr.
He has become fixated on the idea and no longer listens to any advice.
When it is about determination, 'verbissen' (dogged) is often combined with verbs of action. Typical phrases are 'verbissen kämpfen' (to fight doggedly), 'verbissen arbeiten' (to work doggedly), 'verbissen diskutieren' (to argue doggedly), or 'ein Ziel verbissen verfolgen' (to pursue a goal doggedly).
Die beiden Mannschaften kämpften verbissen um den Sieg.
The two teams fought doggedly for victory.
To describe a tense facial expression, 'verbissen' (grim) is usually used with nouns for the face or parts of it. Common combinations are 'eine verbissene Miene' (a grim expression), 'ein verbissener Gesichtsausdruck' (a grim facial expression), or 'mit verbissenem Blick' (with a grim look).
Mit verbissener Miene verfolgte er das Rennen am Bildschirm.
With a grim expression, he followed the race on the screen.
loose / relaxed
'locker' and 'verbissen' describe an attitude toward something. 'locker' means that someone stays relaxed and does not take everything too seriously. 'verbissen' is the opposite: someone is very strongly fixed on a goal and comes across as hard, tense, or inflexible. 'locker' fits well when someone stays calm and open. 'verbissen' fits when someone absolutely wants to win or achieve something and no longer shows any lightness.
Paul trainierte verbissen für den Wettkampf und gönnte sich kaum Ruhe.
Paul trained doggedly for the competition and hardly allowed himself any rest.
Trotz der Prüfung blieb Lisa locker und machte erst einmal eine Pause.
Despite the exam, Lisa stayed relaxed and took a break first.