Most of the FTL feats I've seen for game Sonic come from laser dodging feats, yet for some reason, these haven't all been calculated yet. I'll have two sections: one for the beams that might be lasers and one for the definite lasers. All the scans can be found here.
Oil Ocean Boss
To measure anything here we need Classic Sonic's height.
Modern Sonic is 100 cm. We can look at this image to see that Sonic is 5'1" and Classic Sonic is 3'3" (these aren't accurate measurements, because 3'3" is 100 cm, but this is just for a ratio.) Therefore, Classic Sonic is 76.4 cm, or 0.764 meters.
Classic Sonic is 46 px, the laser was 46 px away, and he jumped 43 px to dodge the laser. Classic moved 0.714 meters.
(0.714) x (299,790,000) / (0.764) = 280,238,478.2608696 m/s, or 93.4% the SoL. Relativistic+.
Classic Sonic is 53 px, the distance is 227 px, or 3.272 meters.
Classic Sonic moves 141 px as shown here. That'd be 1.984 meters.
(1.984) x (299,790,000) / (3.272) = 181,838,532.4306869 m/s, or 60.6% the SoL. Relativistic+.
To compare anything here we need the height of the Eggrobo.
Here's Sonic compared to the Eggrobo. Sonic is 119 px, Eggrobo is 194 px. Eggrobo is 1.245 meters.
In the scene the Eggrobo is 94 px. Sonic moves 6 px (0.079 meters) and the laser is 14 px (0.185 meters) away.
(.079) x (299,790,000) / (.185) = 128,018,432.4324324 m/s, or 60.65% the SoL. Relativistic+.
Nega Wisp Armor
This uses the Cyan Laser to perform the shot, and Cyan Laser is literally meant to be a laser and has quite a few reasonings for being a legit laser, but this is confusing because it doesn't act like all the other Cyan Laser attacks, whereas those are straight beams and this is a single bullet.
Then again, this fades away, reflects off the ground, is meant to be a laser, comes from the Cyan Laser, which typically fires lasers, and this gives you Cyan Laser if you defeat the enemy that shoots the attack, so it's powered by it.
Anyhow, the entire pixel scaling can be found here. Sonic is 19 px, and the attack starts 90 px away. The distance therefore is 4.736 meters.
In the pixel scaling collage I show Sonic travels 13.631 meters.
(13.631) x (299,790,000) / (.908) = 4,500,481,817.180617 m/s, or 15.012c. FTL+. Fixed by Mephistus in comments. 2.87814363162198c. FTL.
Due to the angle here, we'll have to calc the size of a Hotaru for the distance.
Here's a pixel scaling image. The Hotaru is 101 px, Classic Sonic is 109 px. The Hotaru is 0.661 meters.
This is a 40 degree angle, so 0.908 meters for the distance.
Now we should find how far he ran. Using this picture we can find out he ran 19 px whereas he's 23 px, or he ran 0.631 meters.
(0.631) x (299,790,000) / (.908) = 208,334,240.0881057 m/s, or 69.493% the SoL. Relativistic+.
Knuckles dodges this one. We'll need his height.
Here's pixel scaling. Sonic is 100 cm at 340 px. Knuckles is 364 px, so he's 107.058 cm.
The distance is 154 px in the left image, Knuckles is 55 px. Thus it's 299.764 meters away.
Knuckles moved 15 px, or 29.19786096256685 cm.
(.291) x (299,790,000) / (1.07) = 81,531,672.89719626 m/s, or 27.19626168224299% the SoL. Relativistic.
The only thing we can measure here is Beta's arm.
To measure that, we need to compare it to Gamma, and find out Gamma's height.
Here's Gamma compared to Sonic. Gamma is 203 px, Sonic is 147 px. Gamma's 138.095 cm.
Here's Gamma compared to Beta's arm. Gamma is 127 px. Beta's arm is 91 px. Beta's arm is 98.950 cm.
Angle is 78 degrees. 0.61097 meters for the distance.
Now we need to find how far Gamma moved.
In this picture, Gamma is 19 px. He moves 44 px, or 3.197 meters.
(3.197) x (299,790,000) / (0.61097) = 1,568,699,985.269326 m/s, or 5.232c. FTL.
Oil Ocean Boss: 93.4%
Beam Rocket: 60.6%
Nega Wisp Armor: 2.87814363162198c