。
Please hard-boil the eggs.
Literal
Egg [topic-は] hard-ly boil-please.
Note that 卵 is marked with は (topic) rather than を (object). This is a natural shift when the eggs are already the topic of conversation rather than a fresh direct object — e.g. when responding to 'how should I cook the eggs?' 固く is the adverbial form of 固い ('hard, firm'), modifying 茹でる ('boil').