You get bonuses for time, it is only alerts and taking hits that will kill your score. Also relying on some of the support item/abilities will also lower your ranking. Tactical Takedowns, high accuracy, headshots, and rescuing prisoners will raise your score for each time it's done. If you don't get spotted or using reflex mode will garner bonuses as well.

The animal rank, for those who care, is not based on your score but based on how you did the mission. If you use a lot of CQC, you get Bear, if you Snipe your enemies from afar you get Wolf (get it? ) and using non-leathal weapons will get you octopus for example.