schlimmstenfalls
at worst
Indicates what will happen in the most unfavorable or worst possible case.
Schlimmstenfalls verpassen wir den Flug und müssen ein neues Ticket kaufen.
At worst, we'll miss the flight and have to buy a new ticket.

at worst
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at worst
Indicates what will happen in the most unfavorable or worst possible case.
Schlimmstenfalls verpassen wir den Flug und müssen ein neues Ticket kaufen.
At worst, we'll miss the flight and have to buy a new ticket.

The word is composed of 'schlimmsten' (superlative of 'schlimm', bad) and the genitive of 'Fall' (case). So it literally means 'of the worst case' or 'in the worst case'.
Wir müssen mit Verspätungen rechnen, schlimmstenfalls fällt der Zug ganz aus.
We have to expect delays; at worst, the train will be canceled completely.
When 'schlimmstenfalls' (at worst) is at the beginning of the sentence (position 1), the conjugated verb follows directly after it in position 2. However, it can also appear after the verb and subject in the sentence.
Schlimmstenfalls müssen wir die Reise absagen.
At worst, we'll have to cancel the trip.
'Schlimmstenfalls' (at worst) is used to describe the most negative of several possible consequences. It often introduces a sentence that describes this scenario.
Nimm einen Regenschirm mit. Schlimmstenfalls regnet es, aber dann bist du vorbereitet.
Take an umbrella with you. At worst, it will rain, but then you'll be prepared.
if necessary
'gegebenenfalls' and 'schlimmstenfalls' both talk about a possible case. The difference lies in how that case is evaluated. You use 'gegebenenfalls' when something happens if it is necessary or if the situation comes up. It sounds neutral. You use 'schlimmstenfalls' when talking about the worst possible consequence. Learners may confuse the words because both feel like 'falls' (if / in case). Remember: 'gegebenenfalls' means something like 'if necessary', while 'schlimmstenfalls' means 'in the worst case'.

Schlimmstenfalls müssen wir den Termin beim Arzt verschieben.
At worst, we will have to postpone the doctor's appointment.
Die Kundin bekommt gegebenenfalls am Montag ihr Geld zurück.
The customer will get her money back on Monday if necessary.