Speed is not a big issue with D2 as you only need 1 meg up and 1 meg down (most players including me do recommend 5 each way though).
Thd Destiny games DO need a high quality internet signal however as in...
NAT.
Data loss rates.
Signal latency/ping.
Jitter
So...
Run a full internet diagnostic looking for issues.
When was the last time you reset your router and then cleared your system's cache to refresh your internet connection.
Have you looked up those error codes you receive on Bungie.net or the Destiny app to bring up a help guide.
English
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I have been playing Destiny for the past 6 years with a internet connection that is not that good with no problems this started late August when they did some update and since then people with good internet are fine but a small number and people like me and some of my clan have not been able to play ate all