For the Giga Gnomes my favorite tactic is to get some distance on them and find a corner or a large chunk of wall or stone and using burst fire to blast them in their head area for critical damage. As the Giga Gnome approaches you back away towards another corner or source of cover; should they drop their Mushroom hammer and point it towards you, indicating that they are powering up their beam weapon, you simply stop firing and sidestep behind your cover or your corner until the beam cuts out again.
I generally suggest keeping the Giga Gnomes in sight, but at a distance, while you vanquish all the smaller Gnomes and save them for last when you don't have to worry about the little guys coming up on your flanks or rear.
For singularities, especially multiple singularities, I can't stress how handy a good pair of headphones can be in avoiding them. All Singularities emit a deep thrumming noise which gets louder as they close in on you and with a good pair of headphones you should be able to tell just by listening where the singularities are around you and how close, enabling you to concentrate on shooting your Gnome opponents until the audio cue tells you that a singularity is practically right on top of you.
Also you should become familiar with how the singularities behave; each one has a different character to it;
The Green Singularity is unconcerned with you and will simply slowly wander the field without purpose. It will not react to you or chase you in any fashion so you can safely fight near it if you must as long as you keep any eye on how and where it is wandering.
The Red Singularity specifically hunts the closest Player, moving at a constant but slow speed and using the shortest path towards you at all times. You should not attempt to pass close to it or fight near it unless you are forced to do so.
The Yellow Singularity will actually stay motionless unless approached by a Player. When you get within a certain close distance it will then immediately begin moving towards that Player at a fairly quick pace and will continue to move until all Players have moved outside of the range where it can detect you. If you learn the exact "safe" distance from this singularity you may fight near it or pass by it and it will not react to your presence.
The Blue Singularity will actively hunt the closest Player in the same manner as the Red Singularity with one notable difference; when the closest Player is far away it will move with increased speed to close that distance as quickly as possible and once the closest Player is within a certain distance it will then adjust to a slow speed as it continues to approach. Because of the variable speed at which this Singularity moves Players will have a shorter respite from moving to a far corner of the map and will need to more actively track this Singularity's whereabouts.
Another good tactic for both solo Players and groups is for the Players to move towards one end, or corner, of the map during Waves which do not feature Floaties, and quickly vanquish any Gnomes which have spawned in the chosen area. By doing so the opponents, and any singularities, can only approach from a smaller number of directions which can be kept in your field of view, reducing the possibilities that you will be flanked, surrounded, or caught unaware from behind.
