Offer, at least, to make the attempt (3)
I believe the answer is:
bid
This could be a double definition.
'offer at least' is the first definition.
'bid' can be an answer for 'offer' (synonyms). I'm not sure about the 'at least' bit.
'the attempt' is the second definition.
(bid is a kind of attempt)
'to make' is the link.
Can you help me to learn more?
(Other definitions for bid that I've seen before include "Try" , "Offer (for); demand" , "Offer a sum of money to buy" , "Attempt, offer" , "Offer a price" .)