Way, way late here:
OK, we're off to a great start. The very opening is just a bit suggestive without being vulgar. Both Zapp and Kif are in character, especially the latter is great.
Typo/grammar check: Kif's line is great, but "emptied them" is a bit weird since Zapp only mentioned one vat.
“That’s because they’re mermaids!” Kif said.
I'm laughing hard!
"He may have to mop up Zapp’s messes" This would be better with "might," since it's in the past tense. It's a great paragraph, though.
Another line that made me literally LOL: "Aren't you always purple?"
Typo: "and knew she was settled down for the night –loyal in her own way" needs a space after the dash. Lovely line, though.
"Well. Zapp told him to have fun." Another good line, but I think you should have "had told" him here, since it refers to something in the past.
"and he was convinced that Kif was having a good time on his own. Being responsible. Kif loved doing that, didn’t he?" Absolutely hilarious and perfect.
Lots of hilarious scenes and little phrases here.
The climax feels a bit hastily written, but it doesn't really need any more detail. The very ending is hilarious.
I have very little constructive criticism to give, other than the few typoes/technical issues I've pointed out. Great set-up, many good jokes and funny scenes. Very good writing, too, as is to be expected from you. You bring the cruise ship to life without needing paragraphs of description.
It's great seeing a fic focused on Kif (that seems a bit rare in this fandom), and his characterisation is just perfect. I can't praise it enough. He and Zapp play off each other well, and his interaction with Amy is sweet.
In short, a very well-written and entertaining story that gives Kif some well-deserved limelight. Recommended to everyone else.