Here is the full list of all 25 Her Majesty's SPIFFING achievements.
Look intently at Sub Lieutenant Jones
Observe Schrödinger's cat both alive and dead
Complete Her Majesty's SPIFFING: The Empire Staggers Back
Place washing liquid inside washing machine before it's activated
Acquire a second block of cheese
Fail to catch a frog even when they are asleep
Put frogs to sleep
Summon the Power of Greyskull to distract Antoine and Pierre
Examine all the rocks on the planet surface
Maybe it was earth all along?
Locate the French camp while driving the Beagle Two Too
Find the replacement motor
Save game progress using the typewriter
Break a sweat when using the treadmill
Use the ladder like a boss
Wake up Sub Lieutenant Jones
Ensure no one can erase the driver
Crush a table top football player
Crash into ejected fuel cell when at the controls of the HMSS Imperialise
Give Sub Lieutenant Jones English's tea
Attempt to mix washing up liquid and tea
Talk to G.E.R.T.E.A. about British villains
Examine the Gravity Simulation Switch
Locate the paperclip
Commence your mission on board the HMSS Imperialise!