Reapers are a tough one to kill.
Here is a step by step guide on the how to.

Items needed:
1. Stasis rifle
2. Survival knife or Thermal blade (this won't work vs Sea dragons)
3. Large Air tank
4. SeaGlide

Optional
4. extra air tank
5. Spare batteries

Approach the Reaper in your Moth, wait until it notices you. Hop out of your moth with your rifle ready, and line up a small shot (short click) and fire. If you do it right, the Reaper is now trapped for a few seconds in place. Use this time to charge the rifle to maximum (takes 5% of energy) and trap it in place for good.
Now switch to your Seaglide and swim around its head. (It still can and will bite you if you approach it from the front). Once you are behind its head, Do another fully charged shot at its head. Now switch to the knife and start slashing.
You can get 20-22 hits in before you need to renew the stasis field (count every hit). Fully charged Stasis shot at the head again, and continue knifing.
Normal Reapers will/should die before you run out of oxygen if you use a thermal blade.

For Ghost Leviathans, switch to the spare tank around 15 seconds when you have refreshed the stasis field and you can get another 10 slashes in.

Sea dragons: Same method, just use a normal knife, as they are immune to the thermal blade.