EDIT 17.04.2020: was too lazy for a long time (sorry) to edit the Solution but the original requierement for the Achievement were: "get every campaign medal in the game". Since the requierements changed I added the description for every multiplayer medal below.
Credit goes to the Ace Combat Subreddit that helped me with Medal Nr. 21 and Nr. 19 and compiling this list. Thanks to everyone
As a tip for some of those medals: I used a SU-57 with PLSL as main weapon for most things. Bermuda Polygon has given good tips for the machine gun and no damage run in the comments. i suggest everyone to look it up, many thanks to him for that.
Singleplayer Medals
01: Bronze Ace - awarded for destroying 1000 enemy hostiles
02: Silver Ace - Awarded for destroying 2000 enemy hostiles
03: Gold Ace - Awarded for destroying 3000 enemy hostiles
04: Bronze Marksman - Shoot down 50 aircraft with a machine gun
05: Silver Marksman - Shoot down 200 aircraft with the machine gun
06: Gold Marksman - Shoot down 300 aircraft with the machine gun
07: Bronze Wings - Earn an S Rank on all missions on Normal difficulty
08: Silver Wings - Earn an S Rank on all missions on Hard difficulty
09: Gold Wings - Earn an S Rank on all missions on Ace difficulty
10: Raze the Roof - Awarded for destroying 1500 enemy surface targets (excluding ships)
11: Ship of Liberty - Awarded for sinking 100 enemy ships
12: Ghostbuster - Shoot down 200 enemy drones
13: Mass Destruction - Awarded for taking out more than 30 UAVs in mission 03
14: Silence is Golden - Break through the anti-air radar net within 3 minutes in mission 04
15: First Try - Destroy 50 or more ground targets without replenishing supplies in mission 06
16: Relieved - Awarded for completing the rescue mission before 7 distress signals were sent in mission 07
17: Guardian - Awarded for completing mission 10 after destroying 16 or more ground targets
18: Clairvoyant - Awarded for destroying five missile silos withing 5 minutes in mission 13
19: Woah Man! - awarded for completing mission 15 without taking damage
20: Getting The Job Done - Take out Mihaly within 5 minutes in mission 18 without using special weapons
21: Dropping The Bird - Don't use machine gun against arsenal bird in mission 19
22: Piloted - Use only the machine gun for mission 20.
23: Not a Scratch - Awarded for completing the campaign without taking damage
24: Machine Gun Maniac - Awarded for completing campaign with only machine guns (EDIT:Machine Gun Pods and the Puls Laser from the ADF do also count as machine guns)
25: Photon Blitz - Awarded for completing the campaign mode within 4 hours
Multiplayer Medals
01: Bronze Ace - Shoot down 50 rival aircraft
02: Silver Ace - Shoot down 100 rival aircraft
03: Gold Ace - Shoot down 200 rival aircraft
04: Bronze Wings - Sortie in multiplayer mode 25 times
05: Silver Wings - Sortie in multiplayer mode 50 times
06: Gold Wings - Sortie in multiplayer mode 100 times
07: Sky Stalker - Come first in Battle Royal 3 times
08: Victorious and Glorious - Win 50 Team Death Match games
09: All for the Glory - Be the MVP in Team Death Match
10: Say It Cloud and Proud - Receive each of the performance evaluations "Escape Artist", "Cloud Seeker", and "Hide and Seeker" three times or more
If someone has some specific questions just write me a message over xbl.