No offense, but that part was pretty easy!
Spoiler below.... but it's been repeated like 50 times above
The way I did it, an easy way too, was to wait untill red went away, ran thru room, and jumped on closing door. It hurts, yes, but bacta tanks are nice, very nice. The red wont hurt you, and you can simply hop on without the door opening suddenly and you not timing it correctly. Oh, you dont need the gogles for the cave, alothough they are usefull