In Digimon Links, Digimon have weaknesses and resistances. It is very important to be aware of your Digimon's weaknessess and resitances because it can double or half damage you do or damage done to you. Digimon's weaknesses are displayed as blue icons and resistances as red icons in your Digimon's stats screen.
You can add an extra resistance to a Digimon by going into the Digivice's training menu and selecting 'Resist Upgrade'. This requires a Digimon of the exact same kind as the one you want to add a resistance to which will be sacrificed together with some digifuel. The resulting extra resistance on the base Digimon is completely random. You can re-try this as many times as you like until you get the resistance you want, given you have enough materials and sacrifical Digimon.
MEGA Digimon do not need another copy of themself to be sacrificed to get another resistance. Instead they require their own Digifuel and smaller digivolve materials.
IMPORTANT: Extra resistances are lost when awakening, so it is recommended to only resist upgrade +4 Rookie Digimon.
This chart was kindly provided by reddit user /u/CruleD to use on Growlmon.Net. Keep in mind that some MEGA Digimon have special weakness/resistance that do not fit this typical model.
Example: Alphamon does not have any elemental weakness!)
Resistance training costs the same in regular digifuel no matter which awakening level your Digimon is. The only Digimon that has a different resistance training cost is Volcanicdramon. MEGA Digimon also require their own fragments, read more about that below!
*MEGA Digimon also require their own fragments as an additional cost for resistance training. This cost varies depending on the stage of awakening your Digimon is at when you train its resistance.